University of Toronto Linear Algebra Quiz

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