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

What is a Matrix? Definition of Matrix: A ______________of numbers in ____and______. Ex): Matrix A below has two rows and three columns. A= [ ] 2 rows [ ] 3 columns Note: * The _______________of matrix A are 2 X 3 (read “2 by 3” ) * The numbers in a matrix are its_____________. Ex.) The entry in the second row and third column is 5.

Special Matrices (plural) Matrix: Only 1- row ex.) [ ] Matrix: Only 1-column ex.) [ 1 ] [ 3 ] Matrix: The same number of rows and columns. ex.) [ 4 -1 ] [ 2 0 ] Matrix: Matrix whose entries are all zeros. ex.) [ 0 0 ] [ 0 0 ]

Are this two boxes of chocolates equal? ? =

Why are this two boxes of chocolates equal? ? = How many rows of chocolates does each box have? ________________ How many columns of chocolates does each box have?_________________ Look at every chocolate of each box, a.) Are there the same number of chocolates in each box?_____ Are there the same number of rows and same number of columns?______ b.) Are the chocolates in the corresponding positions the same?__________ Then, what can you conclude about the boxes? ____________________________________________ How does this relate to matrices? _______________________________________________________

Equal matrices __________________: Two matrices are EQUAL if their DIMENSIONS are the SAME and the ENTRIES in CORRESPONDING POSITIONS are EQUAL. ex.) [ 5 0 ] equal to? [ 5 0 ] [-4/4 3/4] [ -1.75] Solution: ____________________________________________________ ex.) [-2 6] equal to? [-2 6 ] [ 0 -3] [ 3 0 ] Solution: ____________________________________________________

Adding and Subtracting Matrices Rule: _____or ______matrices if they have the ___________DIMENSIONS. Steps: To add or subtract matrices, you simply add or subtract corresponding entries. ex.) [ 3 ] [ 1 ] [-4] + [ 0 ] [ 7 ] [ 3 ] Solution: __________________________ ex.) [ 8 3 ] _ [ 2 -7] [ 4 0 ] [ 6 -1] Solution: ________________________________________

What is a scalar? Definition of a __________: A real number. Steps: To multiply a matrix by a scalar, simply multiply each entry in the matrix by the scalar. (Process called scalar multiplication.) ex.) Perform the indicated operation. [ -2 0] 3 [ 1 4] = [ 0 3] Solution: _______________________________________________

Solving a Matrix Equation: Ex.) Solve the matrix equation for x and y: [ -2X -8] equal to [ 6 y ] [-10 -9] [-10 -9] Solution: Notice that if this matrices are equal, then the entries in the corresponding positions are also equal. Therefore, _____= 6 solve for x X =________ and ___= y Thus, the value of X is ____and y is ____.

Properties of Matrix Operations Let A,B, and C be matrices with the same dimensions and let c be a scalar. When adding matrices, you can regroup them and change their order without affecting the result. 1.) Associative Property of Addition: (A + B) + __= A + (B + C) 2.) Commutative Property of Addition: ___+ B = B + A Multiplication of a sum or difference of matrices by a scalar obeys the distributive property. 3.) Distributive Property of Addition: ____(A + B) = cA + cB 4.) Distributive Property of Subtraction: c( _______ ) = cA - cB

Guided Practice Problems: Note to the teacher: See section 4.1: Matrix operations 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.