Question

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

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

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

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?

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?

find eigenvalues and eigenvectors of the matrix ((0.6 0.4),(0.2
0.8))

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.

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 =

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

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