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WorksheetsEigenvalues & Eigenvecto
Total questions: 11
Worksheet time: 20mins
Name
Class
Date
1.
If A is a square matrix Ax=λx for nonzero scalar λ, then x is an eigenvector of A
a)
True
b)
False
2.
If λ is an eigenvalue of matrix A, then linear system (A-λI)v=0 has only trivial solution.
a)
True
b)
False
3.
If λ is an eigenvalue of matrix A, then the eigenspace of A corresponding to λ is the set of eigenvectors of A corresponding to λ
a)
True
b)
False
4.
If 0 is an eigenvalue of a matrix A, then A2 is singular
a)
True
b)
False
5.
The eigenvalues of matrix A are the same as the eigenvalues of RREF of A
a)
True
b)
False
6.
If 0 is an eigenvalue of matrix A, then the set of columns of A is linearly independent
a)
True
b)
False
7.
Find eigenvalues for matrix A
a)
λ=1,3
b)
λ=-1,2
c)
λ=1,-2
d)
λ=1,4
8.
Find the eigenvectors for matrix A corresponding to the smallest eigenvalue.
a)
v={r(0,2),r∊R, r≠0}
b)
v={r(1,0),r∊R, r≠0}
c)
v={r(0,1),r∊R, r≠0}
d)
v={r(1,2),r∊R, r≠0}
9.
Find the dimension of eigenspace/geometric multiplicity for matrix A.
a)
1
b)
2
c)
3
d)
4
10.
Find the eigenvalues for A9 of matrix A
a)
λ=1,1/8,512
b)
λ=1,1/2,2
c)
λ=1,1/512,512
d)
λ=1,0,512
11.
Find the eigenvalues AT and A-1 of matrix A
a)
AT: λ=1,4,7
A-1: λ=1,1/4,1/7
A-1: λ=1,1/4,1/7
b)
AT: λ=1,5,9
A-1: λ=1,1/5,1/9
A-1: λ=1,1/5,1/9
c)
AT: λ=0,5,8
A-1: λ=0,1/5,1/8
A-1: λ=0,1/5,1/8
d)
AT: λ=1,0,0
A-1: λ=undefined
A-1: λ=undefined
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