High School: Number and Quantity
Vector and Matrix Quantities HSN-VM.C.8
8. Add, subtract, and multiply matrices of appropriate dimensions.
That's pretty self-explanatory.
Both the addition and subtraction of matrices are incredibly easy. If your students ditched class the day you taught addition and subtraction of matrices, they'd probably be right if they just guessed how to do it. Naturally, they're responsible kids and would never dream of ditching a class as enthralling as yours.
The rule is just to add or subtract numbers that are in the same location. So the number in the top left corner is added to or subtracted from the number in the top left corner.
Students should understand one critical concept about the addition and subtraction of matrices of different sizes. It can't be done. Matrices need to have the same numbers of rows and columns to perform those particular operations.
Here are some examples.
As for multiplication, we should be straight with you. It's pretty tricky.
Here's how multiplication works: we move along the top row of the first matrix and down the second row of the second. Multiply the elements, and then add them up.
No, we aren't kidding. We aren't cruel enough to kid about something like this.
So before we even start, in order to be multiplied, the number of columns of the first matrix has to equal the number of rows of the second. Otherwise they can't be multiplied.
You might want to go easy on the students first, and start with square matrices.
First we move across the top row as we move down the first column. The answer goes in the top row, first column.
3 × 2 + 5 × 8 = 46
Now for the top row, second column.
3 × 6 + 5 × 9 = 63
Those are our two numbers for the top row. Now we'll move onto the bottom row of that first matrix, starting with the first column.
1 × 2 + 4 × 8 = 34
And finally, we'll calculate the bottom row, second column.
1 × 6 + 4 × 9 = 42
That means our resulting matrix is .
Students should know that it's not that bad once they get the hang of it. There are two tricks. The first is physically moving your fingers across and down the matrices so we know which numbers to multiply and add. The second is knowing where to put the answer. Just look at which row you multiplied by which column, and that will be where the answer goes.
Finally, students should know not only how to perform these functions, but how to ask for help if they need it. Matrices are friends, but they're not always easy to get along with.
Here is a recap video of multiplying matrices.