Find the characteristic equation and the eigenvalues (and
corresponding eigenvectors) of the matrix. 2 −2 5 0 3 −2 0 −1 2 (a)
the characteristic equation (b) the eigenvalues (Enter your answers
from smallest to largest.) (λ1, λ2, λ3) = the corresponding
eigenvectors x1 = x2 = x3 =
2. Find all eigenvalues and corresponding linearly independent
eigenvectors of A = [2 0 3 4] (Its a 2x2 matrix)
4. Find all eigenvalues and corresponding linearly independent
eigenvectors of A = [1 0 1 0 2 3 0 0 3] (Its's a 3x3 matrix)
6. Find all eigenvalues and corresponding eigenvectors of A =
1 2 3 0 1 2 0 0 1 .(Its a 3x3 matrix)
Find all distinct (real or complex) eigenvalues of A.
Then find the basic eigenvectors of A corresponding to
each eigenvalue.
For each eigenvalue, specify the number of basic eigenvectors
corresponding to that eigenvalue, then enter the eigenvalue
followed by the basic eigenvectors corresponding to that
eigenvalue.
A = 11 −10
17 −15
Number of distinct eigenvalues: ?
Number of Vectors: ?
? : {???}
Use the method of eigenvalues and eigenvectors to find the
general solution to the following system of differential
equations.
x′(t) = 2x(t) + 2y(t) − z(t)
y′(t) = 0 + 3y(t) + z(t)
z′(t) = 0 + 5y(t) − z(t)
In each of Problems 16 through 25, find all eigenvalues and
eigenvectors of the given matrix. 16) A= ( 1st row 5 −1 2nd row 3
1) 23) A= (1st row 3 2 2, 2nd row 1 4 1 , 3rd row -2 -4 -1)