Question

The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system if it exists.

Answer 1

`\begin{gathered} x-8z=-3 \\ y+8z=-3 \end{gathered}`

The system has no solution

Explanation:

We must convert the matrix into a system of linear equations.

Each vertical represents the letters x, y and z, the first the x, the second y and the third the z. The fourth value is the value of the independent term that would be equal to the other expression, just like this:

`\begin{gathered} 1x+0y-8z=-3 \\ 0x+1y+8z=-3 \\ 0x+0y+0z=0 \end{gathered}`

We operate and the system will finally be like this

`\begin{gathered} x-8z=-3 \\ y+8z=-3 \end{gathered}`

The system is left with 3 unknowns (x, y and z) but only two equations, therefore, the system has no solution, since there are more unknowns than equations.