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

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

Multiplying Matrices x

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

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