Question

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. 4x1 8x2

Answer 1

`x_1=12,\;\;\;x_2=-7`

Explanation:

B be an augmented matrix of the given system is:

`B=[A,b]=\left[\begin{matrix}2&4&-4\\5&7&11\end{matrix}\right] \\\text{multiply the 2nd row by}\; (1)/(2)`

`\left[\begin{matrix}1&2&-2\\5&7&11\end{matrix}\right]`

add -5 times the 1st row to the 2nd row

`\left[\begin{matrix}1&2&-2\\0&-3&21\end{matrix}\right]`

multiply the 2nd row by
`(-1)/(3)`

`\left[\begin{matrix}1&2&-2\\0&1&-7\end{matrix}\right]`

add -2 times the 2nd row to the 1st row

`\left[\begin{matrix}1&0&12\\0&1&-7\end{matrix}\right]`

Hence the given system reduces to

`x_1=12,\;\;\;x_2=-7`

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