Multipying Matrices

Scalar multiplication is when you distribute the number outside the matrix to all the numbers inside the brackets.

To multiply matrices, you first need to write a dimension statement. The dimension statement basically states that the columns of the first matrix must match the rows of the other matrix
For example:

     2 x 2              2 x 2                                                                   

             

     

                                                                  

         2 x 2   times    2 x 2 

The numbers highlighted show that the matrices can be multiplied, since the inside numbers are the same.

  2 x 2   times    2 x 2

These numbers become the dimensions for the product matrix.

After you determined that the matrices can be multiplied, then you start to multiply them together. To do this, you would multiply the first row of the first matrix with the column of the second matrix. More specifically, you would multiply the first number of the first row  on the first matrix with the first number of the first column of the second matrix. You then add the products together and thats the first number of the product matrix. You repeat this until all the numbers of both the matrices have been multiplied, giving you your product matrix.