Scalar multiplication
A scalar is a quantity described by a single numerical value. Scalar multiplication is the process of multiplying a matrix by a scalar (number). Scalar multiplication can be applied to any matrix and involves multiplying each element within the matrix by the given scalar.
In general, the multiplication of a matrix by a scalar will appear similar to this: \lambda \begin{bmatrix} a&b\\ c&d \end{bmatrix}= \begin{bmatrix} \lambda a & \lambda b\\ \lambda c & \lambda d\\ \end{bmatrix}
where Lambda, \lambda, represents the scalar quantity.
Examples
Example 1
If A = \begin{bmatrix} 2 & -6 \\ -4 & 3 \end{bmatrix}, determine 3A.
Example 2
Determine \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}.
Example 3
The cost matrix C shows the current cost, in dollars, per square metre of four different manufacturing materials.
C=\begin{bmatrix} 50& 120 & 90 & 70 \end{bmatrix}
Due to an increase in supplier prices, the cost of each material is expected to rise by 8\%. Determine the new cost matrix after the price increase.
A scalar is a quantity described by a single numerical value. Scalar multiplication is the process of multiplying a matrix by a scalar (number).
Scalar multiplication is used to change each element in the matrix by the same factor.
In general, the multiplication of a matrix by a scalar will appear similar to this: \lambda \begin{bmatrix} a&b\\ c&d \end{bmatrix}= \begin{bmatrix} \lambda a & \lambda b\\ \lambda c & \lambda d\\ \end{bmatrix}
where Lambda, \lambda, represents the scalar quantity.