3 Three \(n \times 1\) column vectors are denoted by \(\mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \mathbf { x } _ { 3 }\), and \(\mathbf { M }\) is an \(n \times n\) matrix. Show that if \(\mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \mathbf { x } _ { 3 }\) are linearly dependent then the vectors \(\mathbf { M x } _ { 1 } , \mathbf { M x } _ { 2 } , \mathbf { M x } _ { 3 }\) are also linearly dependent. The vectors \(\mathbf { y } _ { 1 } , \mathbf { y } _ { 2 } , \mathbf { y } _ { 3 }\) and the matrix \(\mathbf { P }\) are defined as follows: $$\begin{gathered} \mathbf { y } _ { 1 } = \left( \begin{array} { l } 1
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7 \end{array} \right) , \quad \mathbf { y } _ { 2 } = \left( \begin{array} { r } 2
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