Question

Write the coeffcient matrix and the augmented matrix of the given system of linear equations.

6x1+ 7x2= 6
2x1- 8x2=4

Answer 1

Coefficient matrix
`=\begin{bmatrix}6&7\\2&-8\end{bmatrix}`

Augmented matrix
`=\begin{bmatrix}\left.\begin{matrix}6&7\\2&-8\end{matrix}\right|\begin{matrix}6\\4\end{matrix}\end{bmatrix}`

Explanation:

The equations of given system of equations are

`6x_1+7x_2=6`

`2x_1-8x_2=4`

Here, coefficients of first equation are 6 and 7, coefficients of second equation are 2 and -8.

So, coefficient matrix is

`\begin{bmatrix}6&7\\2&-8\end{bmatrix}`

In the given equations constants are 6 and 4.

So, the augmented matrix of the given system of linear equations is

`\begin{bmatrix}\left.\begin{matrix}6&7\\2&-8\end{matrix}\right|\begin{matrix}6\\4\end{matrix}\end{bmatrix}`