# How do you multiply #[(1,2,4), (-1,3,0)]*[(2,-4), (3,5), (-1,0)]#?

##### 2 Answers

Here is the method I was taught. (There is a dual method that is also useful.)

#### Explanation:

**Find the first row of the product**

Take the first row of

Now multiply times the first column and add to get the first number in the first row of the answer:

Next multiply times the second column and add to get the second number in the first row of the answer:

(If there were more columns in the second matrix, we would continue this process.)

A this point we know that the product looks like:

**Find the second row of the product**

Find the second row of the product by the same process using the second row of

Make the second row vertical, multiply and add.

gets us

and

So the product is:

**Note**

If there were another row in the first matrix, then we would find a third row for the product.

This method is the dual of the one I used in the other answer.

#### Explanation:

**Find the first column of the product**

Take the first column of the second matrix. Use its entries to build a linear combination of the columns of the first matrix.

(We'll do the same for the second column in a minute.)

First column of second matrix:

Linear combination of the columns of the first matrix:

this is the first column of the product.

A this point we know that the product looks like:

**Find the second column of the product**

Find the second column of the product by the same process using the values in second column of

Second column of second matrix:

Linear combination of the columns of the first matrix:

this is the second column of the product.

So the product is: