4.2 Operations with Matrices

Scalar multiplication

Matrix can be named by a Capital letter.

Here is Matrix A

45.97.118

32716

049

A

Adding and Subtracting Matrices

To add or subtract the matrices must have the same dimension.

Every element in the matrix is added to the same element in the same row and column in the other matrix

2210

675

1231

450

176

401

6710

501

832

Adding and Subtracting Matrices

To add or subtract the matrices must have the same dimension.

Every element in the matrix is subtracted from the same element in the same row and column in the other matrix

101210

477

433

450

176

401

6710

501

832

Increasing the matrix

To increase the size of equations in a matrix we multiply by a scalar. A scalar is a number that multiplies every element in the matrix.

If Find 4B

375

032

721

B

Find 4B

375

032

721

B

122820

0128

2884

4

4*34*74*5

4*04*34*2

4*74*21*4

375

032

721

44

B

B

Find 3C

843

176

502

C

Add

184326

142415

104873

6112

Properties of Matrix Operations

Given any Matrix A,B or C

Commutative Property of Addition

A + B = B + A

Associative Property of Addition

(A + B) + C = A + (B + C)

Distributive Property, with scalar q

q(A + B) = qA + qB

Homework

Page 164 – 166

# 15 – 21 odd,

30 – 32,

45- 55 odd

HomeworkHomework

Page 164 – 166Page 164 – 166

##14 – 22 even, 14 – 22 even,

33 – 35, 33 – 35,

44- 52 even, 44- 52 even,

59 - 62 59 - 62