Question

Consider 3x3 matrix A with eigenvalues -1, 2, 3. Find the trace
and determinant of A. Then, find the eigenvalues of A^{3}
and A^{-1}.

Answer #1

Find all eigenvalues and eigenvectors for the 3x3 matrix
A= 1 3 2
-1 2 1
4 -1 -1

Find all eigenvectors of this 3x3 matrix, when the eigenvalues
are lambda = 1, 2, 3
4
0
1
-2
1
0
-2
0
1

If the determinant of the 3x3 matrix [2c1 -2c2 2c3; a1+6c1
-a2-6c2 a3+6c3; -b1 b2 -b3] is -16, what is the determinant of the
3x3 matrix [a1 b1 c1; a2 b2 c2; a3 b3 c3]?

Find the eigenvalues and eigenvectors of a 3x3 matrix. (Create a
question and solve this step by step)

Q2. Answer this question by hand. Consider the
matrix
matrix A =
2
6
6
7
Determine the eigenvalues and normalized eigenvectors of
A
Compare the trace of A to the sum of the
eigenvalues of A.
Compare the determinant of A to the product of
the eigenvalues of A.
Find
A−1
using elementary row operations. Be sure to indicate the elementary
row operation used at each step of your calculation.
Apply the formula A-1 =
adj(A) = to obtain...

What are the eigenvalues and eigenvectors of the 3x3 matrix [1 1
1], [1 1 1], [1 1 1]

The matrix A=
1
0
0
-1
0
0
1
1
1
3x3 matrix
has two real eigenvalues, one of multiplicity 11 and one of
multiplicity 22. Find the eigenvalues and a basis of each
eigenspace.
λ1 =..........? has multiplicity 1, with a basis of
.............?
λ2 =..........? has multiplicity 2, with a basis of
.............?
Find two eigenvalues and basis.

find all eigenvalues and eigenvectors of the given matrix
A= [3 2 2
1 4 1
-2 -4 -1]

Find the eigenvalues and the eigenvectors corresponding to them
of the matrix
-2
1
3
0
-2
6
0
0
4

Suppose a 3x3 real matrix A=[a b c; d e f; g h i] has
determinant 5. What is the determinant of the 3x3 matrix B=[2a 2c
2b; 2d 2f 2e; 2g 2i 2h]?

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