4.1: matrix operations objectives: students will be able to: add, subtract, and multiply a matrix by...
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4.1: Matrix OperationsObjectives: Students will be able to:• Add, subtract, and multiply a matrix by a scalar• Solve Matrix Equations• Use matrices to organize data
Matrix
A rectangular arrangement of numbers in rows and columns
Dimensions of a Matrix: # rows by # columns
2 X 3 (read 2 by 3)
701
436
Entries: the numbers in a matrix
Square Matrix: a matrix with the same # of rows and columns
What are the dimensions of the matrices below?
1. 2. 3.
32
41
10
7
1
265
305
712
Two matrices are equal if their dimensions are the same and the entries in corresponding positions are equal.
Are the following matrices equal?
1. and 2. and
44
12
17
425.
5.7
53
21
38
10
To add and subtract matrices, add or subtract corresponding entries:
Can only add and subtract if matrices have the same dimensions
Perform the indicated operations:1. 2. 3.
8
9
1
3
4
0
53
02
59
33
84
3179
Scalar Multiplication: multiply each entry of the matrix by the scalar
1.
2.
48
326
41
89
63
92
33
74
1
Solving Matrix Equations: Solve for x and y
1.
Method 1: Simplify inside parenthesis then multiply
Method 2: Multiply scalar then add
80
4848
61
24
21
084
x
y
Solve for x and y:
2118
90
11
5
45
2103
x
y
Properties of Matrix Operations: A, B and C are matrices, c is a scalar
1. Associative Property (regroup)
2. Commutative Property (change order)
3. Distributive Property of Addition
4. Distributive Property of Subtractions
(A+B)+C = A +(B+C)
A + B = B +A
c(A +B) = cA + cB
c(A- B) = cA- cB
Using Matrices to Organize Data:
Use matrices to organize the following data about insurance rates.
This year for 1 car, comprehensive, collision and basic insurance cost $612.15, $518.29 and $486.91. For 2 cars, comprehensive, collision and basic insurance cost $1150.32, $984.16, and $892.51.Next year for 1 car, comprehensive, collision and basic insurance will cost $616.28, $520.39, and $490.05. For 2 cars, comprehensive, collision and basic insurance will cost $1155.84, $987.72, and $895.13.
Use the matrices to write a matrix that shows the MONTHLY changes from this year to next.