Question

construct the augmented matrix that corresponds to the following system of equations.

Answer 1

Given:

$\begin{gathered} 2x+\frac{5y-z}{4}=9...............(1) \\ 2(6z-4x)+y-8=6...............(2) \\ x-(5+z)=5y...............(3) \end{gathered}$

To find:

The augmented matrix

Explanation:

Let us write equations in the standard form.

From 1,

$8x+5y-z=36...........(4)$

From 2,

$\begin{gathered} 12z-8x+y-8=6 \\ 12z-8x+y=14 \\ -8x+y+12z=14...........(5) \end{gathered}$

From 3,

$\begin{gathered} \begin{equation*} x-(5+z)=5y \end{equation*} \\ x-5-z=5y \\ x-5y-z=5............(6) \end{gathered}$

Using the equation (4), (5), and (6),

The augmented matrix,

$\begin{bmatrix}{8} & {5} & {-1} & {36} \\ {-8} & {1} & {12} & {14} \\ {1} & {-5} & {-1} & {5} \\ {} & {} & {} & {}\end{bmatrix}$

Final answer:

The augmented matrix,

$\begin{bmatrix}{8} & {5} & {-1} & {36} \\ {-8} & {1} & {12} & {14} \\ {1} & {-5} & {-1} & {5} \\ {} & {} & {} & {}\end{bmatrix}$