Matrix Addition, Subtraction, and Scalar Multiplication Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
If A=[10−13]A = \begin{bmatrix} 1 & 0 \\ -1 & 3 \end{bmatrix} and B=[241−2]B = \begin{bmatrix} 2 & 4 \\ 1 & -2 \end{bmatrix}, find A−2BA - 2B.

Solution

  1. 1
    2B=[482−4]2B = \begin{bmatrix} 4 & 8 \\ 2 & -4 \end{bmatrix}.
  2. 2
    A−2B=[1−40−8−1−23−(−4)]=[−3−8−37]A - 2B = \begin{bmatrix} 1-4 & 0-8 \\ -1-2 & 3-(-4) \end{bmatrix} = \begin{bmatrix} -3 & -8 \\ -3 & 7 \end{bmatrix}.

Answer

[−3−8−37]\begin{bmatrix} -3 & -8 \\ -3 & 7 \end{bmatrix}
Linear combinations of matrices (like A−2BA - 2B) are computed by first scaling, then adding/subtracting entry by entry. This is the foundation for more complex matrix algebra.

About Matrix Addition, Subtraction, and Scalar Multiplication

Matrix addition and subtraction are performed entry by entry on matrices of the same dimensions. Scalar multiplication multiplies every entry of a matrix by a single number (the scalar).

Learn more about Matrix Addition, Subtraction, and Scalar Multiplication →

More Matrix Addition, Subtraction, and Scalar Multiplication Examples

Example 1 easy

Compute [formula].

Example 2 medium

Compute [formula].

Example 3 easy

Compute [formula].

← All Matrix Addition, Subtraction, and Scalar Multiplication Examples Matrix Addition, Subtraction, and Scalar Multiplication Concept