1.) Solve the following system using Gauss-Jordan eliminatio…
1.) Solve the following system using Gauss-Jordan elimination. Use a parameter if necessary. \[\begin{align*}x+2y-z&=3\\3x-y+4z&=-1\\-x+5y-6z&=7\end{align*}\] 2.) Find the product \(AB\) if \[A=\begin{bmatrix}1&3&7\\2&-1&0\end{bmatrix}\qquad B=\begin{bmatrix}2&-1\\3&4\\1&-5\end{bmatrix}\] 3.) For which value or values of \(a\) does the following matrix fail to have an inverse? \[\begin{bmatrix}a-2&3\\5&a-4\end{bmatrix}\] 4.) Find the inverse of the following matrix. \[\begin{bmatrix}1&0&-1\\1&-2&3\\2&1&0\end{bmatrix}\] Please upload all work as a single PDF to this question. Make sure you show the front and back of the first page to the webcam as well.
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