Question

Consider the following determinant. \begin{vmatrix} 3 & 6 & 1 \ -1 & 0 & 5 \ 0 & 1 & 1 \end{vmatrix} (a) Use technology to evaluate the determinant. (b) Use the determinant to decide whether the matrix has an inverse. Yes, the matrix has an inverse. No, the matrix does not have an inverse.

          Consider the following determinant.
\begin{vmatrix} 3 & 6 & 1 \ -1 & 0 & 5 \ 0 & 1 & 1 \end{vmatrix}
(a) Use technology to evaluate the determinant.
(b) Use the determinant to decide whether the matrix has an inverse.
Yes, the matrix has an inverse.
No, the matrix does not have an inverse.

Consider the following determinant.
3 6 1 -1 0 5 0 1 1
(a) Use technology to evaluate the determinant.
(b) Use the determinant to decide whether the matrix has an inverse.
Yes, the matrix has an inverse.
No, the matrix does not have an inverse.

Added by Douglas C.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Adi S

07/01/2023

Step 1

Using a calculator or software like MATLAB, we can find that the determinant is 3(0*1 - 5*1) - 6(-1*1 - 5*0) + 1(-1*1 - 0*0) = 3(0 - 5) - 6(-1) + 1(-1) = -15 + 6 - 1 = -10. Therefore, the determinant of the matrix is -10. Show more…

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Consider the following determinant: |[3, 6, 1], [-1, 0, 5], [0, 1, 1]| (a) Use technology to evaluate the determinant. (b) Use the determinant to decide whether the matrix has an inverse. Yes, the matrix has an inverse. No, the matrix does not have an inverse.