Given that A =(X-2 1 )
2 X-3
IS a singular matrix,find the value of x.
To determine the value of x for which matrix A is singular, we need to find the value of x that makes the determinant of matrix A equal to zero.
The determinant of a 2x2 matrix can be found using the formula:
det(A) = (X - 2)(X - 3) - (1)(2)
Let's expand the determinant:
det(A) = X^2 - 3X - 2X + 6 - 2
det(A) = X^2 - 5X + 4
To find the value of x that makes the determinant of A equal to zero, we set det(A) = 0:
X^2 - 5X + 4 = 0
To solve this quadratic equation, we can factorize it:
(X - 1)(X - 4) = 0
From this factorization, we can see that X is either equal to 1 or 4.
Therefore, the potential values of X that make matrix A singular are X = 1 and X = 4.