Answer:
A square matrix can be multiplied to the left of a vector matrix to produce another vector matrix.
Step-by-step explanation:
For example, a 2x2 matrix can be multiplied to the left of a column vector matrix with two rows to produce another column vector matrix with rows as follows:
[tex]A=\left[\begin{array}{ccc}2&3\\4&5\end{array}\right] <------- 2x2 - square - matrix[/tex]
[tex]B = \left[\begin{array}{ccc}2\\7\end{array}\right] <-------- 2x1-vector-matrix[/tex]
[tex]A * B =\left[\begin{array}{ccc}2&3\\4&5\end{array}\right] \left[\begin{array}{ccc}2\\7\end{array}\right][/tex]
[tex]A * B =\left[\begin{array}{ccc}(2*2) + (3* 7)\\ (4*2) + (5 * 7)\end{array}\right][/tex]
[tex]A * B =\left[\begin{array}{ccc}(4) + (21)\\ (8) + (35)\end{array}\right][/tex]
[tex]A * B =\left[\begin{array}{ccc}25\\ 43\end{array}\right][/tex]
From the above therefore, A square matrix can be multiplied to the left of a vector matrix to produce another vector matrix.
