Question

Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. [ -2 -3/2 1/2 ] [ 2 4 0 ] [1/2 2 1 ]

Answer 1

To find the determinant of a matrix, use the formula ad - bc. For this matrix, the determinant is -13/2, which is non-zero, so the matrix has an inverse.

Step-by-step explanation:

To find the determinant of a matrix, we can use the formula:

Determinant = ad - bc

For the given matrix, the determinant is:
Determinant = (-2*4*1) - ((-3/2)*2*(1/2)) = -8 + 3/2 = -13/2

The matrix has an inverse if and only if the determinant is non-zero. Since the determinant is -13/2, which is not equal to zero, the matrix has an inverse.