Final Answer:
x = -2 is the value such that the matrix A is singular.
Explanation:
In order to find out x such that the matrix A is singular, we need to understand the concept of singular matrices. A matrix is said to be singular if its determinant is zero. It can also be said that a matrix is singular when its inverse does not exist. Therefore, we need to calculate the determinant of the matrix A to determine if it is singular or not.
The determinant of a 2X2 matrix can be calculated using the formula |A| = (a11*a22) - (a12*a21). In our case, the matrix A is:
A = [3 x -2 -6]
Therefore, |A| = (3*-6) - (-2*x). This simplifies to |A| = -18 + 2x. To make the matrix singular, the determinant must be equal to zero. Therefore, we get 2x = 18 and x = -2. Thus, x = -2 is the value such that the matrix A is singular.