A matrix is an array of numbers. So, we can talk about one matrix or several matrices. So, we have the following system of equations (I have corrected the second equation):
\(\left \{ {{2a-3b=6} \atop {a+b=2}} \right.\)
This system can be written using matrices as follows:
\(\mathbf{Ax}=\mathbf{B}\)
Where:
\(\mathbf{A}=\left[\begin{array}{cc}2&-3\\1&1\end{array}\right]\)
This one has 2 Rows and 2 Columns (that is, a 2 x 2 matrix). On the other hand, \(\mathbf{x}\) is a column vector (that is, a 2 x 1 matrix):
\(\mathbf{x}=\left[\begin{array}{c}a\\b\end{array}\right]\)
Finally, \(\mathbf{B}\) is a column vector (that is, a 2 x 1 matris)
\(\mathbf{B}=\left[\begin{array}{c}6\\2\end{array}\right]\)
So the system is written using matrices as follows:
\(\mathbf{A}\mathbf{x}=\mathbf{B} \\ \\ \left[\begin{array}{cc}2&-3\\1&1\end{array}\right]\left[\begin{array}{c}a\\b\end{array}\right]=\left[\begin{array}{c}6\\2\end{array}\right]\)
