A square matrix A = cos θ - sin θ sin θ cos θ , then which of the following statement is not correct?

A is skew symmetric matrix for θ ∈ R

A is symmetric matrix If θ = n π , n ∈ I

Write down the matrix A = a i j 2 × 3 where a i j = 2 i - 3 j

The order of matrix is 2 × 3 . Therefore, A = a 11 a 12 a 13 a 21 a 22 a 23 = 2 - 3 2 - 6 2 - 9 4 - 3 4 - 6 4 - 9 = - 1 - 4 - 7 1 - 2 - 5

If A = a b - b a , B = - a b - b - a . Find A + B

Matrices A & B are of the same order hence they can be added. The sum of the matrices is obtained by adding the corresponding elements. A + B = a b - b a + - a b - b - a = a - a b + b - b - b a - a = 0 2 b - 2 b 0

If A = 3 2 1 4 , then find 2 A

Given: A = 3 2 1 4 To find 2 A , scalar multiplication with 2 is applied, which involves multiplication of each element by 2 . 2 A = 2 × 3 2 × 2 2 × 1 2 × 4 = 6 4 2 8

If x 2 - 4 x x 2 1 1 = - 3 1 1 1 , then find the value of x .

Two matrices are equal if they are of same order and their corresponding elements are equal. Here, we are given, x 2 - 4 x x 2 1 1 = - 3 1 1 1 ⇒ x 2 - 4 x = - 3 ⇒ x 2 - 4 x + 3 = 0 ⇒ x - 3 x - 1 = 0 ⇒ x = 3 , 1 Also, x 2 = 1 ⇒ x = 1 , - 1 As the value of x must satisfy both the equations, therefore x = 1 .

Let A = 1 - 1 3 2 - 4 - 3 - 5 - 8 - 11 . Find A T

A T represents transpose of A which is obtained when the rows are changed to columns. A = 1 - 1 3 2 - 4 - 3 - 5 - 8 - 11 Here, R 1 → 1 - 1 3 changes to C 1 i.e., 1 - 1 3 . Similarly, C 2 & C 3 are 2 - 4 - 3 and - 5 - 8 - 11 Hence, A T = 1 2 - 5 - 1 - 4 - 8 3 - 3 - 11