Section 1.4 Matrix Form
A linear system
\begin{align*}
3x_2-6x_3+6x_4+4x_5\amp=-5\\
3x_1-7x_2+8x_3-5x_4+8x_5\amp=9\\
3x_1-9x_2+12x_3-9x_4+6x_5\amp=15
\end{align*}
can be written as
\begin{equation*}
\begin{pmatrix}
0 \amp 3 \amp -6 \amp 6 \amp 4 \amp -5 \\
3 \amp -7 \amp 8 \amp -5 \amp 8 \amp 9 \\
3 \amp -9 \amp 12 \amp -9 \amp 6 \amp 15
\end{pmatrix}\left(\begin{array}{c}
x_1\\
x_2\\
x_3\\
x_4\\
x_5
\end{array}\right)=\left(\begin{array}{c}
-5\\
9\\
15
\end{array}\right)
\end{equation*}
The journey of matrix theory begins!
