Matrix Operations McDougal Littell Algebra 2 Larson, Boswell, Kanold, Stiff Algebra 2: Applications, Equations, Graphs

Review:What is a Matrix? Definition of Matrix: A rectangular arrangement of numbers in rows and columns. Ex): Matrix A below has two rows and three columns. A= [ 6 2 -1 ] 2 rows [-2 0 5 ] 3 columns Note: * The DIMENSIONS of matrix A are 2 X 3 (read “2 by 3” ) * The numbers in a matrix are its ENTRIES. Ex.) The entry in the second row and third column is 5.

Multiplying Matrices If____ is an m X n matrix and _____ is an n X p matrix, then the product ______is an m X p matrix. A * B = AB m X n n X p m X p Conclusion: The ______ of two matrices is defined iff the number of in A is _______to the number of in B.

Let’s Practice: Product defined? State whether the product AB is defined. Explain. Ex.) A: 3X4, B:4X5 Solution: Ex.) A: 3X2, B:5X2

Properties of Matrix Multiplication Let A,B, and C be matrices and let c be a scalar. 1.) Associative Property of Matrix Multiplication: ____(BC) = (AB) C 2.) Left Distributive Property: A( _____ ) = AB + AC 3.) Right Distributive Property: (A + B)___ = AC + BC 4.) Associative Property of Scalar Multiplication: c(AB) = A( __B)

Finding the Product of Two Matrices Ex.) Find AB if A = [ -2 3 ] and B = [ -1 3] [ 1 -4 ] [ -2 4] [ 6 0 ] Solution: AB = [(-2)(-1) + (3)(-2) (-2)(3) + (3)(4)] [(1)(-1) + (-4)(-2) (1)(3) + (0)(4) ] [(6)(-1) + (0)(-2) (6)(3) + (0)(4)] = _______________.

Finding the Product of Two Matrices If A = [3 2] and B = [1 -4], find each product. [-1 0] [2 1] Ex.) AB Solution: AB = [3 2][1 -4] = [-1 0][2 1] ________________ Ex.) BA Solution: BA = [1 -4][3 2] = [2 1][-1 0] ________________ NOTE: ________ DOES NOT EQUAL TO ________

Guided Practice Problems: Note to the teacher: See section 4.2: Multiplying Matrices on the McDougal Littell Algebra II book. Choose the appropriate guided-practice problems for your students.

Solutions to the Guided Practice Problems: Note to the teacher: Include the solutions to the guided-practice problems.