Find the solution of the following matrix equation

Question

Find the solution of the following matrix equation: $Ax = 2x$

While the matrix $A$ is defined as=

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

Any hint?

Answer 1

You simply have to solve the following, where $x=(x_1,x_2,x_3)$ and $I$ is the identity matrix:

$Ax-2x=0$

$(A-I2)x=0$

So, you will get from $(A-I2)$ the matrix:

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

Once you did that, you just have to triangulate through the Gaussian elimination and find your $x$