Warm-Up
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Warm-Up 8 9 1 3 4 0 5 3 0 2 5 9 3 3 4 7 3 6 23 3 9 8 2 9 1 4 1 ) 2 ) 3 ) 4) Name the dimensions 0 8 4 6 2 9 7 5 1 3
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Warm-Up. 3). 1). 4) Name the dimensions. 2). Multiplying Matrices. In order to multiply matrices. A • B = AB. m x n. m x p. n x p. Can you multiply? What will the dimensions be?. A. B. = AB. . 2 x 3. 3 x 4. 2 x 4. A. . = AB. B. 5 x 2. Not possible. - PowerPoint PPT Presentation
Transcript of Warm-Up
Warm-Up
8
9
1
3
4
0
53
02
59
33
4 7 3 6
2 3 3 9 8
2 9 1 4
1)
2)
3)
4) Name the dimensions
08462
97513
Multiplying Matrices
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
A B
A B
= AB
different
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 x 1 1 x 2 2 x 2
2 6
5 15
How to multiply...
fed
cba
mk
ji
hg ag
=+bi +ck ah +bj +cm
2 x 3 3 x 2 2 x 2
dg + ei + fk dh + ej + fm
Ex. 2
10 12 0 21
0 20 0 35
10 0 0 0
2 3
0 5
2 0
K
5 0
4 7M
Find KM
2 21
20 35
10 0
3 x 2
3 x 2 2 x 2
Ex. 3
5 0
4 7
2 3
0 5
2 0
K
5 0
4 7M
Find MK
= ????
Can’t be done
2 3
0 5
2 0
2 x 2 3 x 2
Ex. 4
33
12A
23
10B
Find BA
23
10
30
33
33
12
Ex. 5
40
25
51 4 33 2
6 8x
-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
=
3 1 11
1 2 22
1 0 51
4 1 2
3*1 1*2 1*1
1*1 2*2 2*1
1*1 0*2 5*1
4*1 1*2 2*1
4
7
4
8
EX. 6
3 9 11 0 4
8 0 42 5 0
3 1 5
9 13 21
46 18 18
Ex. 7
What size is the answer? 2 x 3
If the answer is named matrix X, find x22 only! 18Check it out!
HomeworkBack of Yesterday’s
Worksheet with Many Matrices
