Question

find all eigenvalues and eigenvectors of the given matrix

A= [3 2 2

1 4 1

-2 -4 -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

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

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?

Complex Eigenstuff Compute the eigenvalues and eigenvectors for
the given matrix A. List the eigenvalues so the first one has
negative imaginary part. Write the corresponding eigenvectors in
the form [u+iv1]. If there is only one eigenvector, leave the
entries for the second eigenvalue and eigenvector blank. A=[4 -3 3
4]

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 =

The matrix [−1320−69] has eigenvalues λ1=−1 and
λ2=−3.
Find eigenvectors corresponding to these eigenvalues. v⃗ 1= ⎡⎣⎢⎢
⎤⎦⎥⎥ and v⃗ 2= ⎡⎣⎢⎢ ⎤⎦⎥⎥
Find the solution to the linear system of differential equations
[x′1 x′2]=[−13 20−6 9][x1
x2] satisfying the initial conditions
[x1(0)x2(0)]=[6−9].
x1(t)= ______ x2(t)= _____

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

4. Let A = [-5 -5]
[5 -5]
a. Find the eigenvalues and eigenvectors for A.
b. Find an invertible matrix P and a matrix C of the form [a -b]
such that A=PCP-1.
[b a]
c. For the transformation given by T(x) = Ax find the scaling
factor and the angle of rotation.

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