Show that the following system of linear equations is consistent … - Vidyadip

Question

Show that the following system of linear equations is consistent and also find solutions:

x - y + z = 3

2x + y - z = 2

-x - 2y + 2z = 1

✓

Answer

Here,
$\text{x}-\text{y}+\text{z}=3\ \dots(1)$
$2\text{x}+\text{y}-\text{z}=2\ \dots(2)$
$-\text{x}-2\text{y}+2\text{z}=1 \ \dots(3)$
Or, $\text{AX}=\text{B}$
Where,
$\text{A}=\begin{bmatrix}1&-1&1\\ 2&1&-1\\ -1&-2&2\end{bmatrix},\text{X}=\begin{bmatrix}\text{x}\\ \text{y}\\ \text{z}\end{bmatrix}\text{and }\text{B}=\begin{bmatrix}3\\ 2\\ 1\end{bmatrix}$
$\begin{bmatrix}1&-1&1\\ 2&1&-1\\ -1&-2&2\end{bmatrix}\begin{bmatrix}\text{x}\\ \text{y}\\ \text{z}\end{bmatrix}=\begin{bmatrix}3\\ 2\\ 1\end{bmatrix}$
$\text{|A|}=\begin{vmatrix}1&-1&1\\ 2&1&-1\\ -1&-2&2\end{vmatrix}$

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