## Adding and Subtracting Matrices - How it Works - Video

### Theorem on Matrix Properties

Theorem on Matrix Properties:

The important aspect here is that

### Example 1

Example 1:

Our first step when adding or subtracting is to check the dimensions of each matrix. If the matrices are the same, then we can add or subtract. In this case we can add matrix A and matrix B since they are both a 2 x 2 matrix. Now let's add the corresponding elements in each matrix.

==> 1 + -1 ==> 2 + -2

==> 4 + -4 ==> 5 + -5

==> 0 ==> 0

==> 0 ==> 0

Our resultant matrix is a 2 x 2 with zeros in each element. This is called the zero matrix. Any time you have a square matrix, 1 x 1, 2 x 2 , 3 x 3, and ..., and all the elements are zero then it is called the zero matrix.

### Example 2

Example 2:

Our first step when adding or subtracting is to check the dimensions of each matrix. If the matrices are the same, then we can add or subtract. In this case we can add matrix A and matrix B since they are both a 3 x 3 matrix. Now let's add the corresponding elements in each matrix.

==> 1 + -1 ==> 0 + -4 ==> 4 + -3

==> -2 + 0 ==> 5 + -5 ==> 7 + 6

==> 3 + 2 ==> 2 + 4 ==> -1 + -1

==> 2 ==> -4 ==> 1

==> -2 ==> 0 ==> 13

==> 5 ==> 6 ==> -2

Our resultant matrix is a 3 x 3 with the numbers above.

### Example 3

Example 3:

Our first step when adding or subtracting is to check the dimensions of each matrix. If the matrices are the same, then we can add or subtract. In this case we can add matrix A and matrix B since they are both a 3 x 3 matrix. Now let's subtract the corresponding elements in each matrix.

==> 1 - 1 ==> 0 - (-4) ==> 4 - (-3)

==> -2 - 0 ==> 5 - (-5) ==> 7 - 6

==> 3 - 2 ==> 2 - 4 ==> -1 - (-1)

==> 0 ==> 4 ==> 7

==> -2 ==> 10 ==> 1

==> 1 ==> -2 ==> 0

Our resultant matrix is a 3 x 3 with the numbers above.

### Example 4

Example 4:

Our first step when adding or subtracting is to check the dimensions of each matrix. If the matrices are the same, then we can add or subtract. In this case we can add matrix A is a 1 x 3 matrix and matrix B is a 3 x 1 matrix. We cannot subtract these matrices because the number of rows do not match, 1 for A and 3 for B. As well as the number of columns do not match, 3 for A and 1 for B.

So our answer for this question is not possible because they are not the same dimensions.