Warm-up 1.Review notes from Friday. 2.What is the dimension of the matrix below?
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Transcript of Warm-up 1.Review notes from Friday. 2.What is the dimension of the matrix below?
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Warm-up1. Review notes from Friday.
2. What is the dimension of the matrix below?
1 25 10
29 1 18
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Adding, Subtracting, and Scalar Multiplication of
Matrices
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•Only matrices with the same dimensions can be added and subtracted.
•The resulting matrix has the same dimension of the two matrices being added or subtracted.
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Examples
1.
2 0 4
3 10 12
3 2 2
4 6 0
15 2 4
6 7 1
6 6 4
12 8 8
9 5 1
2 4 0 6 4 0
3 15 10 2 12 4
3 6 2 7 2 1
Add the corresponding elements in each matrix
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2. 3 4
0 2
4 6 8
0 2 4
We can’t add because they are different dimensions!!!
3. 2 18
20 5
4 2
5 1
2 ( 4) 18 2
20 ( 5) 5 1
6 20
25 6
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4.
3 10 2
10 8 6
0 1 0
5 4 3
2 1 0
8 10 4
3 5 10 4 2 3
10 2 8 1 6 0
0 ( 8) 1 ( 10) 0 ( 4)
8 6 1
12 7 6
8 11 4
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Scalar Multiplication: each element in a matrix is multiplied by a constant.
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1. 2 7 1 0 -14 2 0
2. 4 2 0
4 5
-8 0
16 -20
3. 5
1 2 3
4 5 6
7 8 9
-5 -10 15
-20 25 -30
35 -40 45
Examples.
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More solving for a variable: A little more complex…
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Upon first glance, these do not look equal. But if we manipulate them, we can see they are equal.
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What pattern do you see? What can we do to get 5 to equal 25?How about 4 to equal 16?
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Homework.Worksheet, problems 1-13.