Khan exercises Maths Tools 1

Homogeneous System with Nontrivial Solution

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For which a\color{red} a does the linear system Ax=0Ax = 0 with A=(a01616664)A= \begin{pmatrix} {\color{red} a} & 0 & -1 \\ -6 & 1 & 6 \\ 6 & 6 & 4 \end{pmatrix} have a nontrivial solution x=(x1x2x3)(000)x = \begin{pmatrix}x_1 \\ x_2 \\ x_3 \end{pmatrix} \neq \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}?