Scalar Multiplication
- When the right conditions are met matrices can be multiplied as well.
- In scalar multiplication, a whole matrix can be multiplied by a scalar (a physical quantity that is completely described by its magnitude).
In the following example a matrix is multiplied by a scalar ‘S’.
\[\Large
A = S
\begin{bmatrix}
2 & 8 & 6 \\
0 & 5 & 4 \\
3 & 7 & 3
\end{bmatrix}
\]
When a matrix is multiplied by a scalar, each individual element in the matrix is multiplied by that scalar and the answer matrix will include the new values as elements.
\[\Large
A = S
\begin{bmatrix}
2 & 8 & 6 \\
0 & 5 & 4 \\
3 & 7 & 3
\end{bmatrix}
\;\;\;\;\;
A = S
\begin{bmatrix}
2S & 8S & 6S \\
0 & 5S & 4S \\
3S & 7S & 3S
\end{bmatrix}
\]
Given below is an example where a matrix A is multiplied by 2:
\[\Large
A = 2
\begin{bmatrix}
2 & 8 & 6 \\
0 & 5 & 4 \\
3 & 7 & 3
\end{bmatrix}
\;\;\;\;\;
A =
\begin{bmatrix}
4 & 16 & 12 \\
0 & 10 & 8 \\
6 & 14 & 6
\end{bmatrix}
\]
What condition need to be satisfied in-order to multiply two matrices?