2.4 Multiplication of a Matrix by a Number

2.4 Multiplication of a Matrix by a Number

When matrix is multiplied by a number, every element in the matrix is multiplied by the number.

Example:

Given that

A = (\begin{matrix} - 2 & 4 \\ 5 & - 6 \end{matrix})

, find each of the following.
(a) 3A
(b) -2A

Solution:

\begin{array}{l} (a) 3 A = 3 (\begin{matrix} - 2 & 4 \\ 5 & - 6 \end{matrix}) \\ = (\begin{matrix} 3 \times (- 2) & 3 \times 4 \\ 3 \times 5 & 3 \times (- 6) \end{matrix}) \\ = (\begin{matrix} - 6 & 12 \\ 15 & - 18 \end{matrix}) \end{array}

\begin{array}{l} (b) - 2 A = - 2 (\begin{matrix} - 2 & 4 \\ 5 & - 6 \end{matrix}) \\ = (\begin{matrix} - 2 \times (- 2) & - 2 \times 4 \\ - 2 \times 5 & - 2 \times (- 6) \end{matrix}) \\ = (\begin{matrix} 4 & - 8 \\ - 10 & 12 \end{matrix}) \end{array}