Chapter 4

Section 3

Matrix Multiplication

Scalar Multiplication

• Scalar Product - multiplying each element in a matrix by a scalar (real number)– Symbol: cA

• Example:

071020

01012153

281

603;

541

732BA

Find 5A – 3B for

Solve

24

010

12

4324X

Matrix Multiplication• Multiplication is only possible if the number of

columns in the first matrix is equal to the number of rows in the second matrix.– Example:

• a 2x3 matrix multiplied by a 3x5 matrix is possible– we say it is defined

• A 4x6 matrix multiplied by a 4x7 matrix is not possible – we say it is undefined

• The product (or resulting) matrix has the dimensions of the rows of the first matrix by the columns of the second matrix.– a 2x3 matrix multiplied by a 3x5 matrix would result in

a 2x5 matrix.• Order Matters!!! AB≠BA

Example of Matrix Multiplication:(pay close attention and write notes that make sense to you)

14131211

10987

65

43

21

05

33

43

01