# Precalculus : Find the Sum or Difference of Two Matrices

## Example Questions

### Example Question #11 : Find The Sum Or Difference Of Two Matrices

Explanation:

The first step in solving this problem is to multiply the matrix by the scalar. The formula is as follows:

In order to add matrices, they have to be of the same dimension.

In this case, they are both 2x2. So, we can then add the matrices together. The result is as follows:

### Example Question #12 : Find The Sum Or Difference Of Two Matrices

We consider  and  defined as follows where they are supposed to be of order .

What is the sum of  and ?

Explanation:

We can perform the addition since the matrices have the same sizes.

Looking at the first row of entries we get:

Note that any entry in the sum of  is equal to .

Thus the sum becomes:

### Example Question #13 : Find The Sum Or Difference Of Two Matrices

We consider the matrices  and  of the same size .

Find the sum .

Explanation:

Note: For addition of matrices, we do it componentwise.

Note: Adding the first two columns of  and  we obtain  for every row of the first column of the resulting matrix.

In all other case, we obtain 0 everywhere. This gives the matrix:

### Example Question #14 : Find The Sum Or Difference Of Two Matrices

We will consider the two matrices  and  given below.  and  are of the same size.

Find the sum

Explanation:

Adding componentwise (adding entry by entry) we obtain zeros everywhere except for the last row where we get  to obain  in every component of the row.

This gives the matrix:

### Example Question #15 : Find The Sum Or Difference Of Two Matrices

We consider the two matrice, find the sum .

We can't add A and B since they are not matrices

Explanation:

Since A and B have the same size, we can perform addition.

The entry located at  (i,j) of matrix A  is added to the entry located at (i,j) of the matrix B.

In this case i=1 and j=1, 2 ,3 ,4,5

performing this operation we obtain:

### Example Question #16 : Find The Sum Or Difference Of Two Matrices

We consider the matrices  and  given below. Find the sum .

,

Explanation:

Since A and B have the same size, we can perform addition.

The entry located at  (i,j) of matrix A  is added to the entry located at (i,j) of the matrix B.

Performing this operation we obtain:

### Example Question #17 : Find The Sum Or Difference Of Two Matrices

For the matrices below, find the sum  ( and  are assumed to have the same size) .  is assumed to be an odd positive integer.

Explanation:

Since we are assuming that the two matrices have the same size, we can performthe matrices addition.

We know that when adding matrices, we add them componenwise. Let (i,j) be any entry of the addition matrix. We add the entry from A to the entry from B:

since the entries from A are the same and given by 1 and the entries from B are the same and given by , we add these two to obtain :

and we know that m is odd integer, hence .

Therefore the entry of the sum matrix is 0

Therefore our matrix is given by:

### Example Question #21 : Matrices

Simplify:

Explanation:

Matrix addition is very easy! All that you need to do is add each correlative member to each other. Think of it like this:

Now, just simplify:

### Example Question #1 : Matrices

Simplify:

Explanation:

Matrix addition is really easy—don't overthink it! All you need to do is combine the two matrices in a one-to-one manner for each index:

Then, just simplify all of those simple additions and subtractions: