Multiplying Matrices Algebra 2—Section 3.6

Recall: Scalar Multiplication - each element in a matrix is multiplied by a constant. Multiplying one matrix by another has a few more “rules” to follow…

**The product of two matrices is defined if the number of columns in the 1 st matrix is equal to the number of rows in the 2 nd matrix. Dimensions (order) : 3 x 2 2 x 3 These must match. These give the dimensions (order) of your answer.

Dimensions (order) : 2 x 3 2 x 2 *They don’t match so these cannot be multiplied together.* Multiply. Can these be multiplied? Check the order of each!

Examples: 2(3) + -1(5)2(-9) + -1(7)2(2) + -1(-6) 3(3) + 4(5) 3(-9) + 4(7)3(2) + 4(-6) Can these be multiplied? Check the order of each! Now multiply each row of the 1 st matrix by each column of the 2 nd matrix Yes, they can!!

2 x 2 2 x 2 *Answer should be a 2 x 2 0(4) + (-1)(-2)0(-3) + (-1)(5) 1(4) + 0(-2)1(-3) + 0(5) Multiply.

On a side note: We can use matrices to write a system of equations. This is useful when solving augmented matrices.

Multiplying Matrices Song (to the tune of “Oh my Darling, Clementine”) Row by column, row by column Multiply them line by line Add the products for an entry Now you’re doing it just fine

Homework:  p  #6-15 multiples of 3, #20, 22, 30