Question

Find solution of equation by using the gaussian elimination method.

2x+3y+z=2

-x+2y+2z=1

x-y-2z=-1

Answer 1

The augmented matrix for the set of equations is:

$\begin{bmatrix} 2 & 3 & 1 & 2 \\ -1 & 2 & 2 & 1 \\ 1 & -1 & -2 & -1 \end{bmatrix}$

Rearranging the rows:

$\begin{bmatrix} 1 & -1 & -2 & -1 \\ 2 & 3 & 1 & 2 \\ -1 & 2 & 2 & 1 \end{bmatrix}$

Multiply the first row by -2 and add it to the second row:

$\begin{bmatrix} 1 & -1 & -2 & -1 \\ 0 & 5 & 5 & 4 \\ -1 & 2 & 2 & 1 \end{bmatrix}$

Add the first row to the third row:

$\begin{bmatrix} 1 & -1 & -2 & -1 \\ 0 & 5 & 5 & 4 \\ 0 & 1 & 0 & 0 \end{bmatrix}$

The third row translates to:

$y=0$

Therefore, the second row translates to:

$5z=4$

$z=4/5$

The first row then translates to:

$x-2(4/5)=-1$

$x-8/5=-1$

$x=-1+8/5$

$x=3/5$