3.6 multiplying matrices
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3.6 Multiplying Matrices. Objective: You will multiply matrices. In order to multiply matrices. A • B = AB. m x n. m x p. n 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. - PowerPoint PPT PresentationTRANSCRIPT
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3.6 Multiplying Matrices
Objective: You will multiply matrices.
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In order to multiply matrices...
A • B = ABm x n n x p m x p
Can you multiply? What will the dimensions be?
2 x 3 3 x 4
AB
5 x 3 5 x 2
2 x 4
Not possible
Ex 1.
A B
A B AB
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How to multiply...
b
a c d
ac=
ad
2 x 1 1 x 2 2 x 2
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How to multiply...
b
a c d
ac=
ad
2 x 1 1 x 2 2 x 2
bc bd
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Ex. 1
5
2 1 3
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Ex. 2
20
14A
21
34B
-16 + 1
0 - 4
-12 +2
0 - 2
-15
- 4-2
-10=
Find AB
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Ex. 3
33
12A
23
10B
Find BA
23
10
30
33
33
12
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How to multiply...
fed
cba
mk
ji
hg ag
=+bi +ck ah +bj +cm
2 x 3 3 x 2 2 x 2
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How to multiply...
fed
cba
mk
ji
hg ag
=+bi +ck
dg +ei +fk
ah +bj +cm
dh +ej +fm
2 x 3 3 x 2 2 x 2
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Ex. 4
40
25
51
86
34
-1(4)+5(6)
5(-3) +2(8)5(4) +2(6)
0(4) +-4(6) 0(-3)+-4(8)
-1(-3) +5(8) -4+ 30
-15 + 1620 +12
0 + -24 0 + -32
3 + 40
26
132
-24 -32
43
=
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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!!
3 1 11
1 2 22
1 0 51
4 1 2
1
2
1
3*1 1*2 1*1
1*1 2*2 2*1
1*1 0*2 5*1
4*1 1*2 2*1
+
+
+
+
+
+
+
+
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3 9 12 3 5
2.) 8 0 41 6 8
3 1 5
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)
33 23 39
21 1 15
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3 9 11 0 4
3.) 8 0 42 5 0
3 1 5
9 13 21
46 18 18
Ex. 5
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What are your questions?
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Assignment