Answer:
Infinitely solution exists,
Required solution is, [tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]
Step-by-step explanation:
We have the given equations:
[tex]x_1+2x_2+8x_3=8[/tex]
[tex]x_1+x_2+4x_3=4[/tex]
Here, the augmented matrix is :
[tex]\left[\begin{matrix}1&2&8&8\\1&1&4&4\end{matrix}\right][/tex]
Now, find the echelon form of the augmented matrix.
[tex]=\left[\begin{matrix}1&2&8&8\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_2-R_1}[/tex]
[tex]=\left[\begin{matrix}1&0&0&0\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_1+2R_2}[/tex]
Therefore, [tex]x_1=0[/tex]
[tex]-x_2-4x_3=-4[/tex]
[tex]\Rightarrow x_2=4(1-x_3)[/tex]
Let [tex]x_3=t[/tex], then the required solution is
[tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]
