Matrix Addition, Subtraction, and Scalar Multiplication Math Example 1

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

Example 1

easy
Compute [1234]+[5678]\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}.

Solution

  1. 1
    Step 1: Add corresponding entries: aij+bija_{ij} + b_{ij}.
  2. 2
    Step 2: [1+52+63+74+8]=[681012]\begin{bmatrix} 1+5 & 2+6 \\ 3+7 & 4+8 \end{bmatrix} = \begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix}.
  3. 3
    Check: Each entry is the sum of the entries in the same position ✓

Answer

[681012]\begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix}
Matrix addition adds corresponding entries element by element. Both matrices must have the same dimensions for addition to be defined.

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 2 medium

Compute [formula].

Example 3 easy

Compute [formula].

Example 4 medium

If [formula] and [formula], find [formula].

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