Q 8. - Precalculus Enhanced with Graphing Utilities

Question

Write the augmented matrix of the given system of equations.

$\left\{\begin{array}{l}9x-y=0\\ 3x-y-4=0\end{array}\right.$

Step-by-Step Solution

Answer

The solution is $\left[\begin{array}{cc}9& -1\\ 3& -1\end{array}\begin{array}{c}|\\ |\end{array}\begin{array}{c}0\\ 4\end{array}\right]$.

Step 1. Given information.

The given system of equations is $\left\{\begin{array}{l}9x-y=0\\ 3x-y-4=0\end{array}\right.$.

Step 2. Rearrange the system of equations.

The required equation is $\left\{\begin{array}{l}9x-y=0\\ 3x-y=4\end{array}\right.$.

Step 3. Determine the augmented matrix.

An augmented matrix is used to represent a system of linear equations.

For writing an augmented matrix, the variables of each equation in the system of equations must be on the left side of equal sign and constants on the right side.

A variable that does not appear in the equation has a coefficient zero.

Hence, the required augmented matrix is $\left[\begin{array}{cc}9& -1\\ 3& -1\end{array}\begin{array}{c}|\\ |\end{array}\begin{array}{c}0\\ 4\end{array}\right]$.