Question

Find the solution of the system of linear equation by using augmented matrix.

\left. \begin{array} { l } { x _ { 1 } - 2 x _ { 2 } = 0 } \\ { 3 x _ { 1 } + 4 x _ { 2 } = - 1 } \\ { 2 x _ { 1 } - x _ { 2 } = 3 } \end{array} \right.

Answer 1

$x_1-2x_2=0$

$3x_1+4x_2=-1$

$2x_1-x_2=3$

augmented matrix:

$\begin{pmatrix} 1& -2&|&0 \\ 3& 4&|&-1 \\ 2& -1&|&3 \end{pmatrix}$

subtract first row multiplied by 3 from second row; subtract first row multiplied by 2 from third row:

$\begin{pmatrix} 1& -2&|&0 \\ 0& 10&|&-1 \\ 0& 3&|&3 \end{pmatrix}$

so, we get:

$10x_2=-1$ and $x_2=1$

this means that the system has not solutions