Holtlinalg1 61026nva consider the matrix a find the

7. –/3 pointsholtlinalg1 6.1.026.nva
Consider the matrix A
Find the characteristic polynomial for the matrix A . (Write your answer in terms of
λ
=
0 0 1
1 0 0
0 1 0
.
.)
(No Response)
Find the real eigenvalues for the matrix A . (Enter your answers as a comma-separated list.)
λ
= (No Response)
Find a basis for each eigenspace for the matrix A
[1;1;1]
.
A =
0 0 1
1 0 0
0 1 0
,
1
1
1

8. –/1 pointsHoltLinAlg1 6.1.037.
Determine if the statement is true or false, and justify your answer.
An eigenvalue
λ
must be nonzero, but an eigenvector u can be equal to the zero vector.
9. –/1 pointsHoltLinAlg1 6.1.039.
Determine if the statement is true or false, and justify your answer.
If u is a nonzero eigenvector of A , then u and A u point in the same direction.
True. Since u is a nonzero eigenvector of A , there exists
λ
> 0 such that A u =
True. Since u is a nonzero eigenvector of A , there exists
λ
< 0 such that A u =
False. A u and u are perpendicular.
False. If
λ
< 0, then A u and u point in opposite directions.
False. If
λ
> 0, then A u and u point in opposite directions.
λ
< 0, A =
− 1 0
0 0
u = ,
1
0
A u = − u
and
λ
u .
λ
u .
.