Demonstrate an Understanding of

ConceptsAddition, Subtraction &

Multiplication by a Scalar

Finite X/A: Unit 6 Day 1

Matrix

Eagles Saints

Rush Yards 112 118Pass Yards 225 284Total Yards 337 402Turnovers 2 2Time of Pos. 33:03 27:57

Football Stats Matrix

Eagles Saints

Rush Yards 112 118Pass Yards 225 284Total Yards 337 402Turnovers 2 2Time of Pos. 33:03 27:57

112 118

225 284

337 402

2 2

33: 03 27 :57

Definition of a Matrix

• An m by n matrix is a rectangular array of elements arranged in m rows and n columns such that it can be written as…

11 12 1

21 22 1

1 1

...

...

...

n

n

m m mn

a a a

a a aA

a a a

Dimensions of a Matrix

• Listed as...

Row x Column

Equal Matrices

• Two matrices are equal if…– They have the same dimension– They have the same exact numbers in all

corresponding positions

Equal or not equal?

4 2

1 8

5 0

4 1 5

2 8 0

Adding Matrices

• Matrices can only be added if…

• To add them, add each number in the corresponding position and then write the sum in that corresponding position of the new matrix.

Adding Matrices Example

8 1

5 14 0 2

1

2 7

430

17

9 4

5 4

2

Multiplication by a Scalar

• As we saw before, matrices are denoted by capital letters.

• Sometimes you will see a problem like this…

, Find 3A.

This is called scalar multiplication

2 1

0 4A

How to Multiply by a Scalar

• To perform scalar multiplication, multiply every element of the matrix by the scalar

2 1 6 33

0 4 0 12A A

More Scalar Multiplication

• You may also see matrices written as such…

This still means scalar

multiplication…

Multiply by 4

4 2

4 2 5

0 8

Subtracting Matrices…

• To subtract matrices, combine scalar multiplication with matrix addition…

5 2 3 4 1 8

5 2 3 1 4 1 8

5 2 3 4 1 8

5 4 2 1 3 8 1 3 11

Closure

• What is/are…– A (the) Matrix?– The dimensions of a matrix?– Equal Matrices?– Matrix Addition and Subtraction?– Scalar Multiplication?