4.1 Using Matrices

Warm-up (IN)

Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar products of matrices.

Evaluate each expression for a=-5, b=1.3 and c=-7.

1. a+b 2. b-c 3. a-b+c 4. -4b

Solve each equation:

5. 16=2x-5 6. 3y+8=-y-15

-3.7 8.3 -13.3 -5.2

x=10.5

y=-5.75

Matrix –

Notes

Dimensions –

Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar products of matrices.

A rectangular array of #s enclosed in single set of brackets

columnsrows ##

431

807

532row

column

33

Entry (or element) – each # in the matrix

1135

9108 32address –

21mrow 2

column 1

5

Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar products of matrices.

2 matrices are equal if they have the same dimensions and corresponding entries are equivalent

EX 1 – Solve for x and y:

1127

15921

1327

15954

yy

x

54 x 21x4 16x 4

32 y 12y

15 y3y 5

EX 2 –

01022

3162 and

3111

295Let NM

NM find a.

3 15 2933 9 3

NM find a.

7 3 3311 11 3

Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar products of matrices.

EX 3 – .2 find

1002

631

023

Let AA

6 4 02 6 124 0 20

Scalar Multiplication

Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar products of matrices.

EX 4 – Represent the quadrilateral as matrix R

E(-4,4)

F(3,1)

H(-4,-3) G(0,-4)

R

E

44

F

31

G

0

4

H

43

Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar products of matrices.

EX 5 – Graph the polygon that is represented by the matrix described below

a. 3R

R

44

31

0

443

1212

93

0

12129

b. 1/3R

3

4

3

4

1

3

1

0

3

4

3

4

1

Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar products of matrices.

HW – p. 221-224 #13-45 odd, 59-62, 66

Out – explain how to represent a polygon in the coordinate plane as a matrix.

Summary – today I learned…