Lesson 9 Multiplying matrices Multiplying matrices A matrix

Lesson 9 Multiplying matrices

Multiplying matrices • A matrix A can be multiplied by another matrix B if the number of columns in matrix A is the same as the number of rows of matrix B. (the inside numbers must be the same) • (3 x 2 ) (2 x 2) • The product is determined by the 2 outside numbers • ( 3 x 2) x (2 x 2) = 3 x 2

Product matrix • When 2 matrices can be multiplied, the product is said to be defined. The matrix that results is called a product matrix. • Determine if the product of the matrices is defined: • Matrix A : 4 x 3, Matrix B: 3 x 1 • Matrix A: 3 x 1 , Matrix B: 2 x 1 • Matrix A: 1 x 5, Matrix B: 5 x 1

Matrix multiplication • Any element in a particular row and column of the product matrix is the sum of the product of the corresponding elements in the corresponding row and column of the matrices being multiplied • These can be done much easier on the calculator

Multiplying matrices • A = 2 -3 B= 1 2 • 3 1 4 -5 • 4 5 • AB = 2(1)+(-3)(4) 2(2) + (-3)(-5) = -10 19 • 3(1) +(1)(4) 3(2)+(1)(-5) 7 1 • 4(1)+(5)(4) 4(2)+(5)(-5) 24 -17

• A square matrix is a matrix with the same number of rows and columns. • It has a main diagonal of elements from the top left hand corner to the bottom right hand corner of the matrix. • The multiplicative identity matrix, called I, is a square matrix in which all of the elements are zero except the main diagonal. All the elements of the main diagonal are ones. • The product of any matrix A and the multiplicative identity matrix I is matrix A • AI = IA = A

Practice • With calculator: • Lesson practice p. 57