Eigen values & Eigen vectors

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 an Identity matrix of order 4 are

• 0, 1. 0, 1

• 0, 0, 0, 0

• 1, 1, 1, 1

• none of these

If Eigen values of a matrix are 0, 1, 2 , then matrix will be

• Non-singular

• Singular

• Both

• None of these

If X is the column vector of order n & A is a square matrix of order n, then what is the order of

 $X^TA\ X$  

• 1 X n

• n x n

• n x 1

• 1 x 1

What is the trace of A = [ 2 3 6 ; 9 0 8 ; 6 2 3 ]

• 5

• 11

• 17

• 4

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

 $A^2$  are

• 4, -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 $\pm\sqrt{13}$

• 4 , - 2 $\pm\sqrt{27}$