# Practice: Expressing Linear Equations As Matrices

 1. Express the following set of linear equations as a matrix. {\displaystyle {\begin{aligned}2x+4y=6\\2x+6y=8\end{aligned}}} .mw-parser-output .hidden-begin{box-sizing:border-box;width:100%;padding:5px;border:none;font-size:95%}.mw-parser-output .hidden-title{font-weight:bold;line-height:1.6;text-align:left}.mw-parser-output .hidden-content{text-align:left}solution ${\displaystyle {\begin{bmatrix}2&4\\2&6\end{bmatrix}}{\begin{bmatrix}x\\y\end{bmatrix}}={\begin{bmatrix}6\\8\end{bmatrix}}}$ 3. Express the following set of linear equations as a matrix {\displaystyle {\begin{aligned}4a-b=4\\5a-2b=2\\a+3b=4\end{aligned}}} solution ${\displaystyle {\begin{bmatrix}4&-1\\5&-2\\1&3\end{bmatrix}}{\begin{bmatrix}a\\b\end{bmatrix}}={\begin{bmatrix}4\\2\\4\end{bmatrix}}}$ 2. Express the following set of linear equations as a matrix {\displaystyle {\begin{aligned}2x_{1}+x_{2}+7x_{3}=5\\x_{1}+x_{2}+5x_{3}=3\end{aligned}}} solution ${\displaystyle {\begin{bmatrix}2&1&7\\1&1&5\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\\x_{3}\end{bmatrix}}={\begin{bmatrix}5\\3\end{bmatrix}}}$ 4. Express the following set of linear equations as a matrix {\displaystyle {\begin{aligned}3r-s+t=10\\2r+4t=11\\15r=0\end{aligned}}} solution ${\displaystyle {\begin{bmatrix}3&-1&1\\2&0&4\\15&0&0\end{bmatrix}}{\begin{bmatrix}r\\s\\t\end{bmatrix}}={\begin{bmatrix}10\\11\\0\end{bmatrix}}}$