The number of values of x in - 4 , - 1 , for which the matrix 3 - 1 + x 2 3 - 1 x + 2 x + 3 - 1 2 is singular, is

Step-by-step solution

For the matrix to be singular, its determinant value should be zero 3 - 1 + x 2 3 - 1 x + 2 x + 3 - 1 2 = 0 ⇒ 3 - 2 + x + 2 - x - 1 6 - x + 2 x + 3 + 2 - 3 + x + 3 = 0 ⇒ 3 x + x - 1 x x + 5 + 2 x = 0 ⇒ x 5 + x 2 + 4 x - 5 = 0 ⇒ x = 0 , - 4 But, x = 0 is rejected Hence, only one value in - 4 , - 1