Answer to Question #236800 in Algebra for moe

Question

Consider the system of equations 

 

$\begin{array}{ccc} +x&&+z&=2\\ +x&+y& &=0\\ & +y&+z&=2\end{array}.$

​.

Which of the following statement(s) is/are true?

1. $y= \frac{\textup{det} \begin{bmatrix}2&0&1\\0&1&0\\2&1&1\end{bmatrix}}{\textup{det} \begin{bmatrix}1&0&1\\1&1&0\\1&0&1\end{bmatrix}}$
2. $x=\frac{\textup{det} \begin{bmatrix}2&0&1\\0&1&0\\2&1&1\end{bmatrix}}{\textup{det} \begin{bmatrix}1&0&1\\1&1&0\\1&0&1\end{bmatrix}}$
3. $z=\frac{\begin{array}{cccc}&-\textup{det} \begin{bmatrix}0&2\\1&2\end{bmatrix} &+ \textup{det} \begin{bmatrix}1&2\\0&2\end{bmatrix}\end{array}}{2}$
4. $z=\frac{\begin{array}{cccccc}&\textup{det} \begin{bmatrix}0&2\\1&2\end{bmatrix} &+ \textup{det} \begin{bmatrix}1&2\\0&2\end{bmatrix}\end{array}}{2}$
5. $y=\frac{\textup{det} \begin{bmatrix}1&2&1\\1&0&0\\0&2&1\end{bmatrix}}{2}$

 

Answer 1

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