Practice: Expressing Linear Equations As Matrices

This page contains practice exercises for expressing linear equations as matrices.

1. Express the following set of linear equations as a matrix.

\begin{align} 2x + 4y = 6 \\ 2x + 6y = 8 \end{align}

solution

\begin{bmatrix} 2 & 4 \\ 2 & 6 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 6 \\ 8 \end{bmatrix}

3. Express the following set of linear equations as a matrix

\begin{align} 4a - b = 4 \\ 5a - 2b = 2 \\ a + 3b = 4 \end{align}

solution

\begin{bmatrix} 4 & -1 \\ 5 & -2 \\ 1 & 3 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 4 \\ 2 \\ 4 \end{bmatrix}

2. Express the following set of linear equations as a matrix

\begin{align} 2x_1 + x_2 + 7x_3 = 5 \\ x_1 + x_2 + 5x_3 = 3 \end{align}

solution

\begin{bmatrix} 2 & 1 & 7 \\ 1 & 1 & 5 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 5 \\ 3 \end{bmatrix}

4. Express the following set of linear equations as a matrix

\begin{align} 3r - s + t= 10 \\ 2r + 4t = 11 \\ 15r = 0 \end{align}

solution

\begin{bmatrix} 3 & -1 & 1\\ 2 & 0 & 4 \\ 15 & 0 & 0 \end{bmatrix} \begin{bmatrix} r \\ s \\ t \end{bmatrix} = \begin{bmatrix} 10 \\ 11 \\ 0 \end{bmatrix}

See also