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4.1: Matrix Operations. Objectives: Students will be able to: Add, subtract, and multiply a matrix by a scalar Solve Matrix Equations Use matrices to organize data. A rectangular arrangement of numbers in rows and columns Dimensions of a Matrix: # rows by # columns 2 X 3 (read 2 by 3). - PowerPoint PPT Presentation
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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
MatrixA 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.
3241
1071
265305712
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
441
217
425.
5.7
5321
3810
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.
891
340
53
025933
8431
79
Scalar Multiplication: multiply each entry of the matrix by the scalar
1.
2.
4832
6
418963
923374
1
Solving Matrix Equations: Solve for x and y1.
Method 1: Simplify inside parenthesis then multiply
Method 2: Multiply scalar then add
80
48486124
2108
4x
y
Solve for x and y:
211890
115
45210
3x
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.