Adding and Subtracting Matrices

Adding and Subtracting Matrices

How to add and subtract matrices: examples and their solutions.

Example 1

If A = [1 2 / 3 4] and B = [2 -1 / 0 1], find A + B.

Add the same positioned elements.

Row 1, Column 1:
1 + 2

Row 1, Column 2:
2 + (-1)

Row 2, Column 1:
3 + 0

Row 2, Column 2:
4 + 1

Example 2

If A = [1 2 / 3 4] and B = [2 -1 / 0 1], find A - B.

Subtract the same positioned elements.

Row 1, Column 1:
1 - 2

Row 1, Column 2:
2 - (-1)

Row 2, Column 1:
3 - 0

Row 2, Column 2:
4 - 1

Example 3

If A = [1 2 / 3 4] and B = [2 -1 / 0 1], find 2A - 5B.

Multiply each coefficient
to the elements of each matrix.

Subtract the same positioned elements.

Row 1, Column 1:
2 - 10

Row 1, Column 2:
4 - (-5)

Row 2, Column 1:
6 - 0

Row 2, Column 2:
8 - 5