Question

Write the augmented matrix of the given system of equations.

$\left\{\begin{array}{l}5x-y-z=0\\ x+y=5\\ 2x-3z=2\end{array}\right.$

Short answer

The solution is$\left[\begin{array}{ccc}5& -1& -1\\ 1& 1& 0\\ 2& 0& -3\end{array}\begin{array}{c}|\\ |\\ |\end{array}\begin{array}{c}0\\ 5\\ 2\end{array}\right]$.

Step-by-step solution

Step 1. Given information.

The given equation is$\left\{\begin{array}{l}5x-y-z=0\\ x+y=5\\ 2x-3z=2\end{array}\right.$.

Step 2. Rewrite the system putting the coefficient of the missing variable as zero.

The required equation is$\left\{\begin{array}{l}5x-y-z=0\\ x+y+0·z=5\\ 2x+0·y-3z=2\end{array}\right.$.

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$\left[\begin{array}{ccc}5& -1& -1\\ 1& 1& 0\\ 2& 0& -3\end{array}\begin{array}{c}|\\ |\\ |\end{array}\begin{array}{c}0\\ 5\\ 2\end{array}\right]$.