Add and Subtract Matrices
How to add and subtract matrices: 4 examples and their solutions.
ExampleA + B
A = [1 2 / 3 4]
B = [2 -1 / 0 1]
So A + B = [1 2 / 3 4] + [2 -1 / 0 1].
Add the same position 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
So [1 2 / 3 4] + [2 -1 / 0 1]
= [1 + 2 2 + (-1) / 3 + 0 4 + 1].
1 + 2 = 3
2 + (-1) = 2 - 1 = 1
3 + 0 = 3
4 + 1 = 5
So A + B = [3 1 / 3 5].
ExampleA - B
A = [1 2 / 3 4]
B = [2 -1 / 0 1]
So A - B = [1 2 / 3 4] - [2 -1 / 0 1].
Subtract the same position 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
So [1 2 / 3 4] - [2 -1 / 0 1]
= [1 - 2 2 - (-1) / 3 - 0 4 - 1].
1 - 2 = -1
2 - (-1) = 2 + 1 = 3
3 - 0 = 3
4 - 1 = 3
So A - B = [-1 3 / 3 3].
Example7A
7A is neither adding nor subtracting matrices.
But, to solve the next example,
let's see how to solve 7A.
A = [1 2 / 3 4]
So 7A = 7[1 2 / 3 4].
Multiply 7 to each element.
7⋅1 = 7
7⋅2 = 14
7⋅3 = 21
7⋅4 = 28
So 7A = [7 14 / 21 28].
Example2A - 5B
A = [1 2 / 3 4]
B = [2 -1 / 0 1]
So 2A - 5B = 2[1 2 / 3 4] - 5[2 -1 / 0 1].
For the same position elements,
write
2⋅[element in A] - 5⋅[element in B].
Row 1, Column 1:
2⋅1 - 5⋅2
Row 1, Column 2:
2⋅2 - 5⋅(-1)
Row 2, Column 1:
2⋅3 - 5⋅0
Row 2, Column 2:
2⋅4 - 5⋅1
This is the way to solve 2A - 5B.
2⋅1 - 5⋅2
= 2 - 10
2⋅2 - 5⋅(-1)
= 4 + 5⋅1
= 4 + 5
2⋅3 - 5⋅0
= 6 - 0
2⋅4 - 5⋅1
= 8 - 5
2 - 10 = -8
4 + 5 = 9
6 - 0 = 6
8 - 5 = 3
So 2A - 5B = [-8 9 / 6 3].