Question

Find all eigenvalues and eigenvectors for the 3x3 matrix

A= 1 3 2

-1 2 1

4 -1 -1

Answer #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

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

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

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

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

Consider 3x3 matrix A with eigenvalues -1, 2, 3. Find the trace
and determinant of A. Then, find the eigenvalues of A3
and A-1.

I'm attempting to diagonalize my 3x3 matrix, but with only 2
eigenvectors I am having trouble organizing my A=PDP^-1.
Original matrix [0 0 1] . Calculated eigenvalues: (2,-2) .
Calculated eigenvectors: [1/2] [0] [-1/2]
[0 2 0] [0] [1] . [0]
[4 0 0] [1] [0] [1]
If I only have 2 eigenvalues, what do i put for my 3x3 D
matrix?
What order should I place my Eigenvectors in for my 3x3 P
matrix?

Normally, we start with a matrix and find the eigenvalues and
eigenvectors. But it’s interesting to see if this process can be
performed in reverse.
Suppose that a 2x2 matrix has eigenvalues of +2 and -1 but no
info on the eigenvectors. Can you find the matrix? How many
matrices would have these eigenvalues?

Normally, we start with a matrix and find the eigenvalues and
eigenvectors. But it’s interesting to see if this process can be
performed in reverse. Suppose that a 2x2 matrix has eigenvalues of
+2 and -1 but no info on the eigenvectors. Can you find the matrix?
How many matrices would have these eigenvalues?

Find the characteristic equation and the eigenvalues (and
corresponding eigenvectors) of the matrix. 0 −3 5 −4 4 −10 0 0
4
(a) the characteristic equation (b) the eigenvalues (Enter your
answers from smallest to largest.) (λ1, λ2, λ3) = the corresponding
eigenvectors x1 = x2 = x3 =

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