# Sum of Matrices Calculator

Instructions: Use our step-by-step calculator of the sum of two matrices, by providing your two matrices of the same size .

Modify, if needed, the size of the matrices by indicating the number of rows and the number of columns. Once you have the correct dimensions you want, you input the matrices (by typing the numbers and moving around the matrix using "TAB")

Number of Rows =    Number of Cols =

$$A$$ = \begin{bmatrix} & \\ & \end{bmatrix}

$$B$$ = \begin{bmatrix} & \\ & \end{bmatrix}

Matrices are extremely useful mathematical objects that serve many different purposes. Indeed, with matrices you can solve systems of linear equations, and in general, you can represent linear functions.

Matrices, much like numbers, can be operated with each other. This is, you can add them, subtract them and multiply them, provided that certain basic dimension conditions are met.

And even, provided that you assess that the matrix is invertible, you can divide by a matrix, much like a regular number.

### How do you sum matrices?

Matrices can be added provided that the matrices have the same size. So, if you want to add two matrices, you should follow these steps:

Step 1: Make sure the matrices you want to add are the same size. In order to do so, you need to assess the number of columns and rows for both matrices and make sure that those numbers coincide.

This is the first and second matrices have the same number of rows and the first and second matrices have the same number of columns.

Observe that you can add matrices that are not squared, as long as the two matrices have the same dimensions.

Step 2: Once you know that the two matrices you are adding have the same size, you need to add each corresponding component from each of the matrices.

This is, in order to get the entry on the first row, first column of the sum matrix, you will take the entry on the first row, first column of the first matrix and you add to it the entry on the first row, first column of the second matrix.

And the you do the same for all the components. So you go adding component by component.

### Can you add a 3x3 and 3x4 matrix?

Strictly speaking, you cannot, because a 3x3 and 3x4 matrix do not have the same dimensions. Now, some clever mathematicians argue that you can "extend" the "smaller" matrix 3x3 to "force" it into a 3x4 matrix. Well, lots of words there.

So, definitely you can make sense to trying to add a 3x3 and 3x4 matrix, but for most purposes, we will say that, no, you cannot add them.

And that same would apply when you try to add matrices of different sizes. The answer is NO, you cannot add them, but definitely you can attempt to make sense to such operation.

### Can you subtract matrices?

Yes! Provided that you have matrices that have the same size, you can subtract them. Much like you do with the addition, in order to subtract two matrices you go subtracting component by component.

Not only can you add or subtract matrices, you can also multiply matrices A and B, provided that the number of columns of A coincides with the number of rows of B.