Multiplying Matrices Dr Shildneck Can You Multiply Matrices

Multiplying Matrices Dr. Shildneck

Can You Multiply Matrices? › What do you think has to be true in order to multiply? › What procedure do you think we’d use? › Let’s try this one…

When Can You Multiply Matrices? › Was your answer… ? Then you are WRONG! › The correct answer is…

So, How Do We Multiply Matrices? › First of all, matrices can only be multiplied if the dimensions “match up” correctly. › Unlike addition and subtraction, this does not mean they have to have the same dimensions.

So, How Do We Multiply Matrices? › So, WHEN we CAN multiply matrices? Two matrices can be multiplied if and only if the COLUMNS number of _______ in the first one is EQUAL to the ROWS number of _______ in the second one.

So, How Do We Multiply Matrices? › The easiest way to do a quick check to see if you can multiply is to write the dimensions of each down in order. › If the middle numbers match, you CAN multiply. › Looking further…

So, How Do We Multiply Matrices? › What does the answer look like? › That it, what are the dimensions of the product? The dimensions of the product of two matrices is the ROWS number of _______ in the first by the number of COLUMNS _______ in the second. › In other words, the dimensions are the “outside” numbers

So, now, how do we find the entries? › The reason the columns and rows must match up is the process used to determine the entries. . . › I call the manual process “The Finger Method” Looking back at our original problem…

Next, what will the dimensions First, check theof the answer be? dimensions… 2 x 2 They dimensions will be match…ofsothe weanswer can 2 x 2. multiply! Now draw a BLANK matrix with the correct dimensions for the answer…

nd ROW nd. FIRST nd nd. FIRST stndand nd , 1 2, st COLUMN useuse the 22 the ROW and 12 COLUMN To find the entry for the 2 FIRST ROW COLUMN use FIRST ROW 2 COLUMN the ROW and 2 nd. FIRST (Remember to always start at the beginning of the row and top of the column) COLUMN (Remember to always start at the beginning of the row and top of the column) 1(2) + 2( -1) 1(3) + 2( 5) 4(2) + 2( -1) 4(3) + 2( 5)

= = 1(2) + 2( -1) 1(3) + 2( 5) 4(2) + 2( -1) 4(3) + 2( 5) 0 6 13 22

The Associative Property for Multiplication states (A x B) x C= A x (B x C) For Matrices, this is also true… This means that you can multiply either set first and get the same answer…

Given that we just found… What do you think equals?

The Commutative Property for Multiplication states A x B = B x A But, in this last example we found that it does not hold true. In fact, it is rare for matrices to be commutative with

The Commutative Property Since the Commutative Property for Multiplication does not hold true for Matrices, it is extremely important that you remember… NEVER SWITCH THE ORDER OF MATRICES WHEN MULTIPLYING!!!

More Examples for Multiplication EXAMPLE 2

More Examples for Multiplication EXAMPLE 3

More Examples for Multiplication EXAMPLE 4

More Examples for Multiplication EXAMPLE 5

More Examples for Multiplication EXAMPLE 6

More Examples for Multiplication EXAMPLE 7

More Examples for Multiplication EXAMPLE 8

ASSIGNMENT Assignment #5 Worksheet