question_answer

Assertion (A): Value of x for which the matrix  is singular is -5.

Reason (R): A matrix A is singular if\[\left| A \right|\ne 0\].

A) Both A and R are individually true and R is the correct explanation of A.

B) Both A and R are individually true and R is not the correct explanation of A.

C) 'A' is true but 'R' is false

D) 'A' is false but 'R' is true

E) Both A and R are false.

Correct Answer: C

Solution :

Given matrix A is singular \[\Rightarrow \,\,2\left( x+4 \right)-\left( 0-2 \right)=0\] \[\Rightarrow 2x+8+2=0\] \[\Rightarrow \,\,2x=-10\,\Rightarrow x=-5\] \[\therefore \]Given Assertion [A] is true Also we know that For singular matrix A, \[\left| A \right|=0\] \[\therefore \]Given Reason is false Hence option [C] is the correct answer.