I have posted similar questions that will be genereated once I start the 20 minute quiz, I need just solutions without shown work, thanks

– Question 1

(a) Find the eigenvalues of

A3

1 point

for

A=

[1 4 1 6

0 11 4 2

0 0 15 2

0 0 09

Eigenvalues of

A3

are:

36

35

in increasing order)

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– Question 2

[4 6 5

Given the matrix A = 0 4 4

0 0-2

, which of the following gives the basis for the eigenspace that corresponds to X= 4?

1 point

Select ALL that apply.

2

0

–

-9

0

0

-9

–

0

Question 3

If = 0 is NOT an eigenvalue of an n x n matrix A, which of the following statements can we say is TRUE?

Select ALL that apply.

1 point

The column vectors of A are linearly dependent and therefore form a basis for Rn.

Using row reduction, it is possible to obtain an identity matrix.

The homogeneous system Ax=0 has infinitely many solution.

Ax=b has exactly one solution for every column vector b.

– Question 4

Given a 2 x 2 matrix that has the eigenvalues-5 and -4, and the eigenvectors

(0)

and

respectively, which of the following could represent P and D?

1 point

Select ALL that apply.

OP=

16 -6

9-2

-4 0

and D =

0

-4

0

-66

OP

-2

and D =

0

-5

6 -6

OP=

g

and DE

:-50

0 -4

]

10 .]

OP=

-50

and DE

Question 5

and upon performing some row operations on the transition matrix we obtain:

10.96 0.08

Suppose we’re finding the steady state vector for the transition matrix A =

0.04 0.92

[This question is based on your assigned pre-reading/prep for the upcoming Assignment]

-0.04 0.08

0 0

What is the actual steady state vector?

1 point

O

-A100

12

یا هر

None of these

O

12

8

12