Find k so that the matrix \(\begin{pmatrix} 1 & 2 & k \\ 3 & 4 & 5 \

1.	Find k so that the matrix \(\begin{pmatrix} 1 & 2 & k \\ 3 & 4 & 5 \\ 7 & 10 & 12 \end{pmatrix}\) is a non - singular matrix .
Answer» 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

Find k so that the matrix \(\begin{pmatrix} 1 & 2 & k \\ 3 & 4 & 5 \\ 7 & 10 & 12 \end{pmatrix}\) is a non - singular matrix .

Answer»

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