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Test: Matrices & Determinants - 1


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20 Questions MCQ Test IIT JAM Mathematics | Test: Matrices & Determinants - 1

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Test: Matrices & Determinants - 1 - Question 1

If a matrix A is such that 3 A3 + 2 A2 + 5 A + I = 0, then A-1 is equal to

Detailed Solution for Test: Matrices & Determinants - 1 - Question 1

3A+ 2A+ 5A + I = 0
3A+ 2A+ 5A + AA−1 = 0
A−1 =- (3 A2 + 2 A + 5I)

Test: Matrices & Determinants - 1 - Question 2

Which of the following statements is/are incorrect?

(i) Adjoint of a symmetric matrix is symmetric.     
(ii) Adjoint of a unit matrix is a unit matrix. 
(iii) A (adj a) = (adj A) A = |A|             
(iv) Adjoint of a diagonal matrix is a diagonal matrix. 

Test: Matrices & Determinants - 1 - Question 3

If every minor of order r of a matrix A is zero, then rank of A is

Test: Matrices & Determinants - 1 - Question 4

If the eigen values of a square matrix be 1, - 2 and 3, then the eigen values of the matrix 3A are

Test: Matrices & Determinants - 1 - Question 5

unit matrix

Test: Matrices & Determinants - 1 - Question 6

If the two eigen values of are 3 and 15, what is the third eigen value?

Test: Matrices & Determinants - 1 - Question 7

The eigen values of matrix A = are

Test: Matrices & Determinants - 1 - Question 8

Let Then

Test: Matrices & Determinants - 1 - Question 9

The rank of matrix is

Test: Matrices & Determinants - 1 - Question 10

If A is 3 × 4 matrix and B is a matrix such that A'B and BA' are both defined, then the order of B is

Test: Matrices & Determinants - 1 - Question 11

If ω is the cube root of – 1, then the value of is

Test: Matrices & Determinants - 1 - Question 12

Let identity inλ, where p, q, r and s are constants, then value of t is

Test: Matrices & Determinants - 1 - Question 13

If a = b = c = 0, then the determinant  is divisible by

Test: Matrices & Determinants - 1 - Question 14

If a2 + b2 + c2 = 0 then value of is

Test: Matrices & Determinants - 1 - Question 15

The value of is

Test: Matrices & Determinants - 1 - Question 16

Value of determinant is

Test: Matrices & Determinants - 1 - Question 17

The value of is

Test: Matrices & Determinants - 1 - Question 18

Study the following assertions about a square matrix
(i) The sum of the eigen values of A is equal to its trace
(ii) The product of the eigen values of A is equal to its determinant
(iii) All eigen values of A are non-zero, if and only if A is non-singular
(iv) If A-1 exists, then the eigen-values of A-1 are equal to the reciprocal of the eigen

Q. Which of the following is correct with respect to above assertions?

Test: Matrices & Determinants - 1 - Question 19

The value of the determinant is

Test: Matrices & Determinants - 1 - Question 20

If ω is an imaginary cube root of unity, then the value of is

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