does the matrix A = 3 -8 2 -5 have an inverse if so what
A yes A^-1= 3 8 -2 5
B yes A^-1= -5 8 -2 3
C yes A^-1 = -3 8 -2 5
D no
To determine if a matrix has an inverse, we need to calculate its determinant. If the determinant is non-zero, then the matrix has an inverse.
Let's find the determinant of matrix A:
| 3 -8 |
| 2 -5 |
The determinant is 3*(-5) - (-8)*2 = -15 + 16 = 1.
Since the determinant is non-zero (1 ≠ 0), matrix A has an inverse.
The correct answer is: A) yes A^-1 = 3 8 -2 5