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

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

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{aligned}2x_{1}+x_{2}+7x_{3}=5\\x_{1}+x_{2}+5x_{3}=3\end{aligned}}

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

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