Engineering Board Exam Reviewer · Determinants · medium

For which values of k is the matrix bmatrixk&2\3&k+1 bmatrix singular?

1. k=2 or k=-3
2. k=-2 or k=3
3. k=2 or k=3
4. k=6 or k=-1

Answer

A. k=2 or k=-3

Solution

The matrix is singular when its determinant is zero: k(k+1)-6=0 k2+k-6=0 (k+3)(k-2)=0. So k=2 or k=-3.

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