WorksheetsEigen Values and Eigen Vectors
Total questions: 10
Worksheet time: 18mins
Sum of the Eigen values of a matrix is equal to ----- of the matrix
determinant
product
trace
sum
Eigen vectors corresponding to distinct Eigen values are
linearly independent
linearly dependent
normalized
none of the above
Eigen values of the matrix [ 1 1 1 ; 1 1 1 ; 1 1 1 ] are
0, 0, 0
0, 0, 3
1, 1, 1
0, 0, 1
If the Eigen values of 3 x 3 matrix are 1, 2, 6 , then Eigen values of inverse of the matrix are
1, 2, 36
1, 2, 6
1, 1/2, 1/6
None of these
If A= [ 2 1 0 ; 0 -3 4 ; 0 0 4 ] , then Eigen values of
A2 are4, -9, 16
4, 9, 16
2, -3, 4
None of the above
IF A = [ 1 1 2 ; 1 -2 5 ; 2 5 -3 ], then the Eigen values of A are
4, 3, -3
4, 3, 1
4 , - 4 ±13
4 , - 2 ±27
Eigen values of an Identity matrix of order 4 are
0, 1. 0, 1
0, 0, 0, 0
1, 1, 1, 1
none of these
If the eigen values of 3X3 matrix is 2,5,3 then find detA
30
40
50
20
The determinant |𝐴 − 𝜆𝐼| when expanded will give a polynomial, which we call as ---------
of matrix 𝐴.
Characteristic polynomial
polynomial
linear polynomial
None of the above
The non-zero vector 𝑋 got from (𝐴 − 𝜆𝐼)𝑋 = 0 is called the ------- corresponding to the
Eigen value 𝜆.
latent vector
null vector
unit vector
orthogonal vector
