Question

Find the augmented matrix for the systemIt gives us 3 numbers already

Answer 1

It is required that we find an augmented matrix for the system.

Recall that a matrix that contains the coefficients and constant terms of a system of equations, each written in the standard form with the constant terms to the right of the equals is called an augmented matrix.

The given system of equations is:

`\begin{cases}x+5y+8z=-9 \\ 3x+z=-4 \\ 7x+5y+7z=3\end{cases}`

The first, second, and third equations can be rewritten to get:

`\begin{cases}1x+5y+8z=-9 \\ 3x+0y+1z=-4 \\ 7x+5y+7z=3\end{cases}`

Hence, the augmented matrix using the system is:

`\begin{bmatrix}{1} & 5 & 8 & {-9} \\ {3} & {0} & 1 & {-4} \\ {7} & {5} & 7 & {3} \\ & {} & {} & {}\end{bmatrix}`