JEE Mathematics Online Test Matrices Set D

1. Statement 2: If | A | = 0 then A^–1 does not exist.

2. Statement 1 : (a₁₁, a₂₂, .........a_nn) is a diagonal matrix then A^–1 = dia (a₁₁^–1, a₂₂^–1, a_nn^–1) Statement 2 : If A = dia (2, 1, –3) and B = dia (1, 1, 2) then det (AB^–1) = 3

3.

4. (1) adj (adj A) = A (2) | adj (adj A) | = 1
(3) | adj A | = 1 (4) | adj A | = 2

5. (1) x = 1 (2) y = 2
(3) z = 3 (4) n = 3

6. (1) a = cos 2Θ (2) a = 1
(3) b = sin 2Θ (4) b = 1

7. If A is a matrix of the order 3 and | A | = 8, then | adj A | is equal to

8. The matrix A satisfying the equation

9.

10. If A is a skew symmetric matrix of order n and C is a column matrix of order n × 1, then C^T AC is:

11. The rank of the matrix

12. If a square matrix A is such that AA^T = I = A^T A, then | A | is equal to :