Question

Write the augmented matrix, in correct format, for the system of equations below.6x + 9y + 6z = 544×+2y+7z=173x - 2y + 22 = 2

Answer 1

This system of equations, which consists of three equations and 3 unknowns, can be written in matrix form, as shown below

$\begin{gathered} \begin{bmatrix}{6} & {9} & {6} \\ {4} & {2} & {7} \\ {3} & {-2} & {22}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{54} & {} & {} \\ {17} & {} & {} \\ {2} & {} & {}\end{bmatrix} \\ \Leftrightarrow A\cdot x=b \end{gathered}$

Then, the augmented matrix is

$(A|b)=\begin{bmatrix}{6} & {9} & {6\text{ | }54} \\ {4} & {2} & {7\text{ | }17} \\ {3} & {-2} & {22\text{ | }2}\end{bmatrix}$