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Engineering Maths MCQ - Linear Algebra

21 The vector

is an eigen vector of

-2	2	-3
2	1	-6
-1	-2	0

one of the eigen values of A is

2	0	0	-1
0	1	0	0
0	0	3	0
-1	0	0	4

Sum of the eigen values of the matrix A is

23 Given: Matrix A =

1	6	1
1	2	0
0	0	3

the Largest eigen value is

Now

1-λ	1	1
1	1-λ	1
1	1	1-λ

=0

⇒

3-λ	3-λ	3-λ
1	1-λ	1
1	1	1-λ

=

0

⇒

3-λ

1	1	1
1	1-λ	1
1	1	1-λ

=

0

⇒

3-λ

1	0	0
1	-λ	1
1	0	λ

=

0

Hence eigen values are 0,0,3

24 Corresponding to highest eigen value the eigenvector is

Corresponding to highest eigen value the eigenvector is

A
B
C
D

Repeating above procedure, we get successively RepeaRepeating above procedure, we get successively
ting

RepeaRepeating above procedure, we get successively
ting

It follows that the largest eigen value is 4 and corresponding eigenvector is

25 Given Matrix A=

The eigen-values are

Given Matrix A=The eigen-values are

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Rank of the matrix 0 0 -3 9 3 5 3 1 1

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