Question

Write the augmented matrix of the given system of equations.

Answer 1

Answer::

`\mleft[\begin{array}rrr1 & 1 & -1 & 8 \\ 6 & -4 & 0 & 4 \\ 6 & 2 & -1 & 2\end{array}\mright]`

Explanation:

For any system of equations, an augmented matrix is a matrix of numbers where:

• Each row represents the constants((both the coefficients and the constant) from one equation; and

,

• Each column represents all the coefficients for a single variable.

Given the system of equations:

`\mleft\{\begin{array}{r}x+y-z=8 \\ 6x-4y=4 \\ 6x+2y-z=2\end{array}\mright.`

Writing this as a product of matrices gives:

`\mleft(\begin{array}{rrr}1 & 1 & -1 \\ 6 & -4 & 0 \\ 6 & 2 & -1\end{array}\mright)\mleft(\begin{array}{rrr}x \\ y \\ z\end{array}\mright)=\mleft(\begin{array}{rrr}8 \\ 4 \\ 2\end{array}\mright)`

Therefore, the augmented matrix is:

`\mleft[\begin{array}rrr1 & 1 & -1 & 8 \\ 6 & -4 & 0 & 4 \\ 6 & 2 & -1 & 2\end{array}\mright]`