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

Answer:

Infinitely solution exists,

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

Step-by-step 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

 $(x_1,x_2,x_3)=(0, 4(1-t),t)$