# Linear Algebra - Linear Algebra

21:

Determinant of the matrix

 1 0 0 0 100 1 0 0 100 200 1 0 100 200 300 1

is

 A. 100 B. 200 C. 1 D. 0 Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. priyanka said: (11:00pm on Wednesday 1st July 2015) the given matrix is referred as lower triangular matrix . then the determinant of that type of matrix is the product of diagonal elementsfrom the above given matrix, the diagonal elements are 1,1,1,1the product of 1.1.1.1=1 Write your comments here:
22:

The vector

 1 2 -1

is an eigen vector of

A =

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

one of the eigen values of A is

 A. 1 B. 2 C. 5 D. -1 Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
23:

Given : A =

 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

 A. 10 B. -10 C. 24 D. 22 Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
24:

Given: Matrix A =

 1 6 1 1 2 0 0 0 3

the Largest eigen value is

A.

1

B.

2

C.

3

D.

4

Option: D

Explanation :

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

Click on Discuss to view users comments.