Warm-Up 3) 1) 4) Name the dimensions 2)

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Quiz – you may not use your notes 1) 3) 4) Name the dimensions 2) Check your work!! Watch out for careless errors.

3.6 Multiplying Matrices Algebra II

In order to multiply matrices... A • B = AB m x n n x p m x p 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

If we are multiplying matrices, we multiply each row of the first matrix by each column in the second matrix!!

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

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

Ex. 3 Find BA

How to multiply... ag +bi +ck ah +bj +cm = 2 x 3 3 x 2 2 x 2

2 x 3 3 x 2 2 x 2 = How to multiply... ag +bi +ck ah +bj +cm dg +ei +fk dh +ej +fm 2 x 3 3 x 2 2 x 2

Ex. 4 -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

If we are multiplying matrices, we multiply each row of the first matrix by each column in the second matrix!! multiply each row of the first matrix by each column in the second matrix!! + + 1 + + 2 + + 1 + +

2 X 3 3 X 3 2(3)+(-3)(8)+5(-3) 2(9)+(-3)(0)+ 5(1) 2(1)+(-3)(-4)+ 5(5) -1(3)+(6)(8)+8(-3) -1(9)+(6)(0)+ 8(1) -1(1)+(6)(-4)+ 8(5)

Ex. 5

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