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.