Scalar multiplication
A scalar is a quantity, or a magnitude. When we multiply a matrix by a scalar, we multiply each element in the matrix by the given scalar. In general, the multiplication of a matrix by a scalar will appear similar the following: \lambda \begin{bmatrix} a&b\\ c&d \end{bmatrix}= \begin{bmatrix} \lambda a & \lambda b\\ \lambda c & \lambda d\\ \end{bmatrix}
As an example, the multiplication of a matrix with numerical elements by a scalar will look like the following: 3 \begin{bmatrix} 2&-2\\ 6&0 \end{bmatrix}= \begin{bmatrix} 6 & -6\\ 18 & 0\\ \end{bmatrix} We can see that each element was multiplied by 3.
Examples
Example 1
If A = \begin{bmatrix} 2 & -6 \\ -4 & 3 \end{bmatrix}, find 3A.
A scalar is a quantity, or a constant number.
When we multiply a matrix by a scalar, we multiply each element in the matrix by the given scalar.
Matrices and using the calculator
Matrices allow us to perform numerous calculations in one operation. They are very useful when analysing and keeping track of large amounts of data. For example, we could store information about a large inventory in a matrix. We could then use spreadsheets, calculators or other technology to monitor stock, by using matrix addition to add in orders, subtraction to take away sales and multiplications to calculate revenue, expenses and profit.
Examples
Example 2
Find \dfrac{1}{2}A+\dfrac{2}{3}B if A =\begin{bmatrix} 6&-12\\ 4&14 \end{bmatrix} and B =\begin{bmatrix} 24&3\\ -12&0 \end{bmatrix}.
Matrices allow us to perform numerous calculations in one operation. They are very useful when analysing and keeping track of large amounts of data.