Question

Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) x1 2x2 8x3

Answer 1

Infinitely solution exists,

Required solution is,
`(x_1,x_2,x_3)=(0, 4(1-t),t)`

Explanation:

We have the given equations:

`x_1+2x_2+8x_3=8`

`x_1+x_2+4x_3=4`

Here, the augmented matrix is :

`\left[\begin{matrix}1&2&8&8\\1&1&4&4\end{matrix}\right]`

Now, find the echelon form of the augmented matrix.

`=\left[\begin{matrix}1&2&8&8\\0&-1&-4&-4\end{matrix}\right]^(R_1\rightarrow R_2-R_1)`

`=\left[\begin{matrix}1&0&0&0\\0&-1&-4&-4\end{matrix}\right]^(R_1\rightarrow R_1+2R_2)`

Therefore,
`x_1=0`

`-x_2-4x_3=-4`

`\Rightarrow x_2=4(1-x_3)`

Let
`x_3=t`, then the required solution is

`(x_1,x_2,x_3)=(0, 4(1-t),t)`