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in Applications of Matrices and Determinants by (46.9k points)
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Find k so that the matrix  \(\begin{pmatrix} 1 & 2 & k \\ 3 & 4 & 5 \\ 7 & 10 & 12 \end{pmatrix}\) is a non - singular matrix .

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Let A = \(\begin{pmatrix} 1 & 2 & k \\ 3 & 4 & 5 \\ 7 & 10 & 12 \end{pmatrix}\) Give A is non-soingular. That is |A| \(\ne\) 0

\(\begin{vmatrix} 1 & 2 & k \\ 3 & 4 & 5 \\ 7 & 10 & 12 \end{vmatrix}\) \(\ne\) 0

1(48 - 50) - 2(36 -35) + k(30 - 28) \(\ne\) 0

-2 - 2 + 2k \(\ne\) 0

2k \(\ne\) 4 ⇒ k \(\ne\) 2

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