Warm-up 3.).

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Presentation transcript:

Warm-up 3.)

Multiplying Matrices

In order to multiply matrices... A • B = AB r x c r x c r x c the inside dimensions must be the same! Ex 1. Can you multiply? What will the dimensions be? A B AB 2 x 3 3 x 4 2 x 4 AB A B 5 x 3 5 x 2 Not possible

Identify the dimensions of each matrix Identify the dimensions of each matrix. Then, tell if it is possible to multiply them together.

The #1 Jam in the ATL The Matrix Song To the tune of “My Darling Clemintine”

Multiply them line by line The Matrix Song Row by column, row by column Multiply them line by line Add them up to form a matrix Now you’re doing it just fine

How to multiply... ac ad = 2 x 1 1 x 2 2 x 2

How to multiply... ac ad = bc bd 2 x 1 1 x 2 2 x 2

Ex. 1

sum of pair-wise products How to multiply... ag +bi +ck ah +bj +cm = 2 x 3 3 x 2 2 x 2 sum of pair-wise products

sum of pair-wise products How to multiply... ag +bi +ck ah +bj +cm = dg +ei +fk dh +ej +fm 2 x 3 3 x 2 2 x 2 sum of pair-wise products

Ex. 2

-1(4) +5(6) -1(-3) +5(8) -4 + 30 3 + 40 5(4) +2(6) 5(-3) +2(8) 20 +12 Ex. 3 -1(4) +5(6) -1(-3) +5(8) -4 + 30 3 + 40 5(4) +2(6) 5(-3) +2(8) 20 +12 -15 + 16 = + -24 + -32 0(4) +-4(6) 0(-3) +-4(8) 26 43 32 1 -24 -32

Ex. 4 Find AB -16 + 1 -12 +2 -15 -10 = - 2 - 4 -2 - 4