LA2.1.2

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Find x\, such that {\begin{bmatrix}1&x&1\end{bmatrix}}{\begin{bmatrix}1&3&2\\2&5&1\\15&3&2\end{bmatrix}}{\begin{bmatrix}1\\2\\x\end{bmatrix}}=0\,.

Now {\begin{bmatrix}1&x&1\end{bmatrix}}{\begin{bmatrix}1&3&2\\2&5&1\\15&3&2\end{bmatrix}}{\begin{bmatrix}1\\2\\x\end{bmatrix}}=0\, implies

{\begin{bmatrix}1+2x+15&3+5x+3&2+x+2\end{bmatrix}}{\begin{bmatrix}1\\2\\x\end{bmatrix}}=0\,

{\begin{bmatrix}16+2x&6+5x&4+x\end{bmatrix}}{\begin{bmatrix}1\\2\\x\end{bmatrix}}=0\,

16+2x+12+10x+4x+x^{2}=10,x^{2}+16x+28=0,(x+2)(x+14)=0,x=-2,-14\,


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