Use determinants to decide whether the matrix has an inverse.

Name: Use determinants to decide whether the matrix has an inverse.
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Question

Use determinants to decide whether the matrix has an inverse.
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Quizplus · Accepted Answer

If the determinant of a matrix is non-zero, then the matrix has an inverse. Using the determinant formula for a 3x3 matrix:

| 2  1  3 |
| 1  0 -1 |
| 4 -1  2 |

det = 2(-1)(2) + 1(4)(3) + 3(1)(-1) - 4(-1)(3) - 1(2)(2) - 2(0)(-1) = -12

Since the determinant is non-zero (-12 ≠ 0), the matrix has an inverse.

Use Determinants to Decide Whether the Matrix Has an Inverse