Marg Cardo Started to depet P1000 Quarterly in A Fund that pay 5% compounded Quarterly. How much will be Hi Fund affec 7 year

-What Will be the Future

Answer:

14 cupcakes

Step-by-step explanation:

40 percent of 35 is 14

Answer:

14 cupcakes had sprinkles.

Step-by-step explanation:

Write 40% as 40/100. Since finding the fraction of a number is the same as multiplying the fraction with the number, we have 40/100 of 35 = 40/100 × 35.

By using mean and standard deviation, the results obtained are

a)  The probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean = 0.6212

b) The probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean = 0.7416

c) )The probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean = 0.8904

What is mean and Standard Deviation?

Suppose there is a data set. Mean is the average of the values of the data set.

Variance is the sum of the square of  deviation of the data values from the mean

Square root of variance is the standard deviation.

The Mean Preparation Fee ( \(\mu\) ) for 2017 Federal Income Tax Returns= $273

Standard deviation \(\sigma\) of preparation fees = $100

$16 of mean = 273-16 to 273+16

                      = $257 to $289

(a) The probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean

The formula used for finding the required probability

\(\ P(\$257 < \bar{X} < \$289) = P(\frac{\bar{x}_1-\mu}{\sigma/\sqrt{n}} < z < \frac{\bar{x}_2-\mu}{\sigma/\sqrt{n}}) \\ \ \\ = P(\frac{257-273}{100/\sqrt{30}} < z < \frac{289-273}{100/\sqrt{30}}) \\ \ \\ = P(-0.88 < z < 0.88 ) \\ \ \\ = P(z < 0.88) -P(z < -0.88)\\ \ \\ =0.8106 -0.1894\)

=0.6212

(b) The probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean

\(P(\frac{257-273}{100/\sqrt{50}} < z < \frac{289-273}{100/\sqrt{50}}) \\ \\\ = P(-1.13 < z < 1.13 ) \\ \ \\ = P(z < 1.13 ) -P(z < -1.13 )\\ \ \\ =0.8708 -0.1292 \\ \ \\ =0.7416\)

(c)The probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean

\(P(\frac{257-273}{100/\sqrt{100}} < z < \frac{289-273}{100/\sqrt{100}}) \\ \ \ \\ = P(-1.60 < z < 1.60 ) \\ \ \\ = P(z < 1.60 ) -P(z < -1.60 )\\ \ \\ =0.9452 -0.0548 \\ \ \\ =0.8904\)

To learn more about mean and standard deviation, refer to the link -

https://brainly.com/question/28225633

#SPJ4

Complete Question

The cpa practice advisor reports that the mean preparation fee for federal income tax returns was $273 use this price as the population mean and assume the population standard deviation of preparation fees is $100 use z-table. round your answers to four decimal places. a. what is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean? b. what is the probability that the mean price for a sample of 50 federal income tax returns is within  $16 of the population mean? c. what is the probability that the mean price for a sample of $100 federal income tax returns is within $16 of the population mean? d. which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to have at least a probability that the sample mean is within of the population mean?

Statistical significance refers to the likelihood that the association between two variables is not due to chance alone. In other words, it is a measure of the probability that the observed relationship between two variables is real and not just a result of random variation or sampling error.

When analyzing data, researchers often use statistical tests to determine whether there is a significant association between two variables. A p-value is calculated, which represents the probability that the observed relationship between the variables is due to chance. If the p-value is less than a predetermined threshold (usually 0.05), the results are considered statistically significant, and the researchers can conclude that there is a real association between the variables. It's important to note that statistical significance does not necessarily imply practical significance. Just because a relationship is statistically significant does not mean that it is important or meaningful in real-world terms. Additionally, statistical significance only tells us about the strength of the relationship between two variables, not about causation or directionality. Therefore, it is always important to interpret statistical significance in the broader context of the research question and study design.

Learn more about probability here

https://brainly.com/question/13604758

#SPJ11

Answer:

trapezoid

Step-by-step explanation:

A right trapezoid has 2 parallel sides and 2 adjacent right angles.

In geometry, the base of a prism is the actual shape.

So the base of a triangular prism is the triangle, similarly the base of a pentagonal prism is the pentagon, etc.

Therefore, the base of a trapezoidal prism is the trapezoid itself.

If the prism is cut parallel to the base, then the cross section will be the same shape as the base.  So in this case, it will be a trapezoid.

Answer:

sQUARW

Step-by-step explanation:

The statement describes the percentage of people in the nation who eat out without making any inferences or assumptions.

The statement made by the person is a descriptive statement. This means that the statement simply describes the percentage of people in the nation who always eat out. It does not make any assumptions or inferences based on the data or evidence given. A descriptive statement is one that simply states facts or information without making any assumptions or interpretations about it. It is important to note that a descriptive statement does not imply any cause and effect relationship between the facts or data given. For example, in this statement, there is no inference being made that the people who eat out are healthier or more likely to be successful than people who don't eat out. It is simply stating the percentage of people in the nation who always eat out.

Learn more about percentage here

https://brainly.com/question/16797504

#SPJ4

The distance between two places can be calculated using various methods:

a. Distance = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. Distance = Speed × time taken

As given in the question,

Distance between two places can be calculated using various techniques:

a. If the coordinates of the two points representing the places are given as (x₁ , y₁) and (x₂ , y₂ ) then

distance between two places  = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. If the distance travelled between two place with known speed and time taken to cover that distance then

Distance =  Speed × time taken

If the distance between two places is small then it can be calculated using any measuring scale.

Therefore, the distance between the two given places is given by :

a. Distance = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. Distance = Speed × time taken

Learn more about distance here

brainly.com/question/15172156

#SPJ4

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The coefficient of a¹⁷b²³ in the expansion of (3a−7b)⁴⁰ is 5,727,000,416,289,510,400.

To find this coefficient, we will use the binomial theorem. According to the theorem, the coefficient of a¹⁷b²³ in the expansion of (3a−7b)⁴⁰ is given by the expression: C(40, 23) × (3a)¹⁷ × (−7b)²³, where C(40, 23) is the number of ways to choose 23 objects out of 40. This can be calculated using the formula: C(40, 23) = 40! / (23! × 17!)

Substituting the values, we get:

C(40, 23) = 40! / (23! × 17!)

= (40 × 39 × 38 × ... × 18 × 17!) / (23 × 22 × ... × 2 × 1)

= 5,717,078,887

Therefore, the coefficient of a¹⁷b²³ in the expansion of (3a−7b)⁴⁰ is:

5,717,078,887 × (3a)¹⁷ × (−7b)²³

= 5,727,000,416,289,510,400

Hence, the answer is 5,727,000,416,289,510,400.

To know more about binomial theorem, refer here:

https://brainly.com/question/30100273#

#SPJ11

Answer:

The vertex is (-2,10)

Step-by-step explanation:

The vertex is the maximum point on a downward facing parabola

The maximum is (-2,10)

The vertex is (-2,10)

(100,000 - 10,000) + 1 count for ( from 10,000 means 10,000 is included in it ) + 1 count for ( to 100,000 means 100,000 is also included in it )

= 90,000 + 1 + 1

= 90,002

Answer:

B. 63°

Step-by-step explanation:

The distance around a circle is 360°

This means that 297° + n = 360°

Equation:

297 + n = 360

We can find the value of n by subtracting:

297 + n = 360

-297        -297

n = 63

Therefore, the value of n is 63 degrees.

The required piece-wise function shown in the graph is y = x + 1 for x < 2 and y = 2x - 1 for x > 2.

To determine the equation of the given piece-wise function,
The equation of the function under x < 2 is given as,
y = x + 1 for x < 2

This equation can be obtained by locating two points on the line such as (-1, 0) and (0, 1), and forming an equation with these points,

Similarly,
For x > 2, we have
y = 2x - 1

Thus, the required piece-wise function shown in the graph is y = x + 1 for x < 2 and y = 2x - 1 for x > 2.

Learn more about piece-wise function here:

https://brainly.com/question/22051192

#SPJ1

The diagonal EG is a line of symmetry for rhombus EFGH

A rhombus is a quadrilateral with equal sides. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.

Given rhombus EFGH

We have to prove that diagonal EG is a line of symmetry for rhombus EFGH

According to the property of the rhombus

Four sides of EFGH are equal

So EF = EH

FG =HG

Meanwhile EG =EG(common side)

So triangle EFG = triangle EHG

The diagonal EG is a line of symmetry for rhombus EFGH

Therefore the diagonal EG is a line of symmetry for rhombus EFGH

To learn more about rhombus visit

https://brainly.com/question/27870968

#SPJ1

The equation of the line that passes through the points (0,-2) and (3,2) is  4x-3y-6 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

The points are (0,-2) and (3,2)

To find the equation of the line,

Find slope by using formula  m = (y₂-y₁)/(x₂-x₁)

m = (2-(-2))/(3-0)

m = 4/3

The equation of line is,

y-y₁ = m (x-x₁)

y-(-2) = 4/3(x-0)

y+2 = 4/3x

3y+6 = 4x

4x-3y-6 = 0

The required equation of line is 4x-3y-6 = 0.

To know more about Equation of line on:

https://brainly.com/question/21511618

#SPJ1

To graph the equation y = (1/2)x, we can plot points on a coordinate plane and connect them to create a straight line. Here's how to do it:

1. Choose some x-values to evaluate the equation. Let's select a range of x-values, such as -10, -5, 0, 5, and 10.

2. Substitute each x-value into the equation to find the corresponding y-values. For example:

  - For x = -10, y = (1/2)(-10) = -5

  - For x = -5, y = (1/2)(-5) = -2.5

  - For x = 0, y = (1/2)(0) = 0

  - For x = 5, y = (1/2)(5) = 2.5

  - For x = 10, y = (1/2)(10) = 5

3. Plot the points (x, y) on a graph. In this case, the points would be:

  (-10, -5), (-5, -2.5), (0, 0), (5, 2.5), (10, 5)

4. Connect the plotted points with a straight line. The line should pass through all the points.

The resulting graph is a straight line with a slope of 1/2, passing through the origin (0, 0), and extending infinitely in both directions.

Here is a rough sketch of the graph:

```

   |      

6  |         .

   |       .

5  |     .

   |   .

4  | .  

   |

3  |   .

   |

2  |     .

   |      

1  |       .

   |      

0  -----------------------

  -10 -5  0  5  10

```

Note: The above graph is a visual representation and may not be to scale. The line should pass through the plotted points accurately.

To know more graph , refer here :

https://brainly.com/question/28583246#

#SPJ11

Answer:

x= 7/2

Step-by-step explanation:

move the constant 2x+5=12 to make it 2x=12-5.

subtract 12-5= 7

2x=7 divide both sides

x=7/2

i did try my best hope this helps :)

There are several characteristics that, on their own, do not prove that a quadrilateral PQRS, drawn on a coordinate plane, is a parallelogram.  None of these characteristics individually guarantee that the quadrilateral is a parallelogram.

These characteristics include having equal side lengths, having congruent opposite angles, having a pair of parallel sides, and having diagonals that bisect each other.

While having equal side lengths is a characteristic of a parallelogram, it is not sufficient to prove that PQRS is a parallelogram. The quadrilateral may still have other properties that invalidate it as a parallelogram, such as non-parallel opposite sides or unequal opposite angles.

Having congruent opposite angles is another characteristic of a parallelogram. However, this alone does not guarantee that PQRS is a parallelogram. It is possible for a quadrilateral to have congruent opposite angles while lacking parallel sides or other defining properties of a parallelogram.

Having a pair of parallel sides is a strong indication that a quadrilateral is a parallelogram. However, it is not enough to establish it definitively. The quadrilateral may still have other properties that contradict the definition of a parallelogram, such as unequal side lengths or diagonals that do not bisect each other.

Learn more about parallelogram here:

https://brainly.com/question/32441125

#SPJ11

Which characteristics will not prove that quadrilateral is a coordinate plane or it is a parallelogram?.

Answer:

(a) \(x\³ - 6x - 6\)

(b) Proved

Step-by-step explanation:

Given

\(r = $\sqrt[3]{2} + \sqrt[3]{4}$\) --- the root

Solving (a): The polynomial

A cubic function is represented as:

\(f = (a + b)^3\)

Expand

\(f = a^3 + 3a^2b + 3ab^2 + b^3\)

Rewrite as:

\(f = a^3 + 3ab(a + b) + b^3\)

The root is represented as:

\(r=a+b\)

By comparison:

\(a = $\sqrt[3]{2}\)

\(b = \sqrt[3]{4}$\)

So, we have:

\(f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3\)

Expand

\(f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

Evaluate like terms

\(f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)\)

Recall that: \(r = $\sqrt[3]{2} + \sqrt[3]{4}$\)

So, we have:

\(f = 6 + 6r\)

Equate to 0

\(f - 6 - 6r = 0\)

Rewrite as:

\(f - 6r - 6 = 0\)

Express as a cubic function

\(x^3 - 6x - 6 = 0\)

Hence, the cubic polynomial is:

\(f(x) = x^3 - 6x - 6\)

Solving (b): Prove that r is irrational

The constant term of \(x^3 - 6x - 6 = 0\) is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

\(f(-6) = (-6)^3 - 6*-6 - 6 = -186\)

\(f(-3) = (-3)^3 - 6*-3 - 6 = -15\)

\(f(-2) = (-2)^3 - 6*-2 - 6 = -2\)

\(f(-1) = (-1)^3 - 6*-1 - 6 = -1\)

\(f(1) = (1)^3 - 6*1 - 6 = -11\)

\(f(2) = (2)^3 - 6*2 - 6 = -10\)

\(f(3) = (3)^3 - 6*3 - 6 = 3\)

\(f(6) = (6)^3 - 6*6 - 6 = 174\)

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational

The person can get 3 fives, 2 sixes, and 1 two in 336 ways.

To find the number of ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die, we can use the formula for combinations with repetition:

\(C(n + k - 1, k) = C(6 + 3 - 1, 3) * C(3 + 2 - 1, 2) * C(1 + 1 - 1, 1)\)

where n is the number of possible outcomes (in this case, 6), k is the number of choices to make (in this case, 3 for fives, 2 for sixes, and 1 for twos), and C(n + k - 1, k) represents the number of combinations with repetition.

Using this formula, we can calculate:

\(C(8, 3) * C(4, 2) * C(1, 1) = 56 * 6 * 1 = 336\)

Therefore, there are 336 ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die.

You can learn more about combination at

https://brainly.com/question/28065038

#SPJ11

Based on the solution below, we have:

A. a + 2b =5 corresponds to 5. a = 5 - 2b;

B. 5a = 2b  corresponds to 1. a = 2b/5;

C. a + 5 = 2b corresponds to 4. a = 2b - 5;

D. 5(a + 2b) = 0 corresponds to 3. a = -2b; and

E. 5a + 2b=0 corresponds to 2. a = -2b/5.

For clarity purposes, the equations in the question are restated as follows:

A. a + 2b = 5                1. a = 2b/5

B. 5a = 2b                   2. a = -2b/5

C. a + 5 = 2b               3. a = -2b

D. 5(a + 2b) = 0          4. a = 2b-5

E. 5a + 2b =0              5. a = 5-2b

A. From the equation a + 2b = 5, a can be solved as follows:

a + 2b = 5

a = 5 - 2b

B. From the equation 5a = 2b, a can be solved as follows:

5a = 2b

a = 2b/5

C. From the equation a + 5 = 2b, a can be solved as follows:

a + 5 = 2b

a = 2b - 5

D. From the equation 5(a + 2b) = 0, a can be solved as follows:

5(a + 2b) = 0

5a + 10b = 0

5a = -10b

a = -10b/5

a = -2b

E. From the equation 5a + 2b =0, a can be solved as follows:

5a + 2b =0

5a = -2b

a = -2b/5

Learn more about solving an equation: https://brainly.com/question/19297665.

#SPJ1

Answer:

ABD=90

DBC=63

Step-by-step explanation:

set up the equation to find x:

abd+dbc=abc

(5x+5)+(3x+12)=153

calculate equation:

Step 1: Simplify both sides of the equation.

5x+5+3x+12=153

(5x+3x)+(5+12)=153(Combine Like Terms)

8x+17=153

8x+17=153

Step 2: Subtract 17 from both sides.

8x+17−17=153−17

8x=136

Step 3: Divide both sides by 8.

8x /8 =  136 /8

x=17

now we have x, plug it into both angle equations.

ABD=5x+5

5(17)+5=90

DBC=3x+12

3(17)+12=63

John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

Learn more about after-tax rate of return  here:-

https://brainly.com/question/31825431?referrer=searchResults

#SPJ11

Answer:

6 12 18 24 30 36 42 48 54 60

Step-by-step explanation:

Answer:

b. 48

i found the answer key lol

Answer:

Step-by-step explanation:

The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

To learn more about vectors

https://brainly.com/question/13322477

#SPJ4

Answer:

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case.

If two lines in a linear system intersect they have exactly one point in common.

If two lines in a linear system are consistent they occupy the same space at the same time and have all their points in common.

If two lines in a linear system are parallel, they do not have any points in common.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 5 - 9 is an equation.

We have,

If two lines intersect they have exactly one solution.

If two lines are parallel they do not have any points in common.

If two lines are consistent the lines are in the same space at the same time and have all their points in common.

Thus,

Option 1 = intersect.

Option 2 = consistent.

Option 3 = parallel.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ6

a basis for the eigenspace corresponding to the eigenvalue λ = 1 is { [4, -2] }, and a basis for the eigenspace corresponding to the eigenvalue λ = 2 is { [0, 0] }.

To find a basis for the eigenspace corresponding to each listed eigenvalue of matrix A, we need to solve the system (A - λI)v = 0, where A is the given matrix, λ is the eigenvalue, I is the identity matrix, and v is a non-zero vector in the eigenspace.

Given the matrix A = [[11, 2], [1, 2]], we will find the eigenspaces corresponding to the eigenvalues λ = 1 and λ = 2.

1) For λ = 1:

We need to solve the equation (A - λI)v = 0.

Substituting λ = 1 and I as the 2x2 identity matrix, we have:

(A - I)v = 0

[[11, 2], [1, 2]] - [[1, 0], [0, 1]] = [[10, 2], [1, 1]]v = 0

To find the basis for the eigenspace corresponding to λ = 1, we need to solve the homogeneous system of equations:

10v₁ + 2v₂ = 0

v₁ + v₂ = 0

One solution to this system is v = [2, -1]. However, since we want a basis (more than one vector), we can multiply this solution by any non-zero scalar. Let's multiply by 2:

v₁ = 4, v₂ = -2

Therefore, a basis for the eigenspace corresponding to λ = 1 is { [4, -2] }.

2) For λ = 2:

We need to solve the equation (A - λI)v = 0.

Substituting λ = 2 and I as the 2x2 identity matrix, we have:

(A - I)v = 0

[[11, 2], [1, 2]] - [[2, 0], [0, 2]] = [[9, 2], [1, 0]]v = 0

To find the basis for the eigenspace corresponding to λ = 2, we need to solve the homogeneous system of equations:

9v₁ + 2v₂ = 0

v₁ = 0

From the first equation, we can see that v₁ = 0. Substituting this into the second equation, we have v₂ = 0 as well.

Therefore, a basis for the eigenspace corresponding to λ = 2 is { [0, 0] }.

To know more about matrix visit:

brainly.com/question/29995229

#SPJ11

Answer:x= 0.5,−3

Step-by-step explanation: