warm-up
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Warm-Up
8
9
1
3
4
0
53
02
59
33
41
89
63
92
33
74
11)
2)
3)
4) Name the dimensions
08462
97513
Quiz – you may not use your notes
84
3179
48
3261)
2)
3)
4) Name the dimensions
2 7 11 14
111
72
37
82
61
61
Check your work!! Watch out for careless errors.
4.3 Multiplying Matrices
“take it row by column”
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
How to multiply...
b
a c d
ac=
ad
2 x 1 1 x 2 2 x 2
How to multiply...
b
a c d
ac=
ad
2 x 1 1 x 2 2 x 2
bc bd
Ex. 1
5
2 1 3
2 6
5 15
Ex. 2
20
14A
21
34B
-16 + 1
0 - 4
-12 +2
0 - 2
-15
- 4-2
-10=
Find AB
Ex. 3
33
12A
23
10B
Find BA – be careful, order matters
23
10
30
33
33
12
How to multiply...
fed
cba
mk
ji
hg ag
=+bi +ck ah +bj +cm
2 x 3 3 x 2 2 x 2
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
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
=
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
+
+
+
+
+
+
+
+
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
3 9 11 0 4
3.) 8 0 42 5 0
3 1 5
9 13 21
46 18 18
Ex. 5
What are your questions?
OK … time to use your knowledge!
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