10.4 Day 1 Matrix Algebra 2011 January 18, 2011 10.4 Matrix Algebra DAY 1 Objectives: 1. Find the sum and difference of two matrices. 2. Find scalar multiples of a matrix. 3. Find the product of two matrices. Nov 9­12:38 PM 1 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Warm­up: Use the shortcut to evaluate each determinant. (Remember...the properties make some problems easier!) 1. 3 ­2 4 ­1 5 0 ­2 6 1 2. 4 5 ­1 8 ­7 3 4 5 ­1 Jan 13­7:43 PM 2 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Arranging Data in a Matrix Read the following statement. I plan to apply to CU Succeed and earn College Algebra credit this semester. When the answer that applies to you is read aloud please stand. YES MAYBE NO Females Males Jan 13­2:36 PM 3 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 State the dimensions of each matrix. 1. [ ] 2. [ ­12 27 0 ] 3. [ ] 4. [ ] 1 0 ­3 0 1 2 8 3 1 14 30 ­15 21 8 ­43 5 ­9 4 ­3 7 0 Jan 13­2:55 PM 4 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 State the dimensions of each matrix. What do these matrices have in common? [ ] 5 ­9 ­3 7 [ ] 1 2 7 ­3 7 ­8 0 9 12 If the number of rows and columns are the same the matrix is called a square matrix. Jan 13­3:26 PM 5 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Find the Sum of Two Matrices ***To add or subtract matrices their dimensions must be the same!!!*** extras 1. [­8 13 2] + [12 ­10 ­7] [ ] 2. [ ] [ ] [ ] 3. [ ] [ ] [ ] ­4 0 11 5 ­9 4 + ­3 7 0 ­2 5 ­3 14 30 ­15 20 + 8 ­43 3 5 2 ­7 ­1 12 Nov 30­12:48 PM 6 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Find the Difference of Two Matrices ***To add or subtract matrices their dimensions must be the same!!!*** extras 1. [ ] [ ] [ ] 2. [ ] [ ] [ ] 3 ­1 9 ­1 ­6 0 ­ 7 1 7 7 5 ­8 1 2 3 4 5 6 7 8 9 ­ 1 ­4 7 2 ­5 8 3 ­6 9 Nov 30­12:48 PM 7 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Zero Matrix [ ] [ ] 0 0 0 0 0 0 0 0 0 0 0 0 [ ] 0 0 0 0 0 0 0 0 0 [0 0 0] [ ] 0 0 0 0 Get it? Jan 13­8:19 PM 8 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Find Scalar Multiples of a Matrix Given the following matrices: extras A = [­1 4 11] [ ] B = 3 ­1 4 ­2 5 ­8 Find each scalar multiple. 1. 3A [­1 4 11] 2. ­2B [ ] 3. 4C [ ] C = 12 7 8 ­10 3 ­1 4 ­2 5 ­8 [ ] 12 7 8 ­10 Nov 30­12:48 PM 9 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Find the Product of Two Matrices Example: Breckenridge sells 1 day lift tickets for the following prices: child $51, adult $89, and senior $79. In one hour, 100 child tickets, 500 adult tickets, and 30 senior tickets are sold. Use matrix multiplication to find the total revenue for one hour. extras [ ] P = [51 89 79] R = PT T = [51 89 79] 100 500 30 [ ] 100 500 30 Nov 30­12:49 PM 10 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Find the Product of Two Matrices Rule: The number of columns in the first matrix must match the number of rows in the second matrix. extras A = [ ] 2 1 3 0 1 ­1 B = [ ] Find the product. 1. AB 1 0 2 1 3 2 [ ][ ] 2 1 3 0 1 ­1 1 0 2 1 3 2 Answer: [ ] 13 7 ­1 ­1 Jan 13­9:08 PM 11 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Find the Product of Two Matrices Rule: The number of columns in the first matrix must match the number of rows in the second matrix. extras A = [ ] 2 1 3 0 1 ­1 B = [ ] Find the product. 1 0 2 1 3 2 2. BA [ ][ ] 1 0 2 1 3 2 1 0 1 ­1 3 2 Answer: [ ] 2 1 3 5 1 6 8 1 9 Jan 13­9:08 PM 12 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Without solving determine the dimensions of each solution. extras A = [­1 4 11] [ ] B = 3 ­1 4 ­2 5 ­8 [ ] C = 12 7 8 ­10 1. A + A 2. A ­ C 3. CB 4. BA Jan 13­9:49 PM 13 10.4 Day 1 Matrix Algebra 2011 January 18, 2011 Homework: page 783 (7 ­ 18, 23 ­ 28) Next Week... Monday: MLK day...NO SCHOOL!! Tuesday: cRAzY hAiR dAy Wednesday: Footie Jammies Day Thursday: TWIN DAY Friday: neon t­shirt day Saturday: GLOW DANCE Jan 13­8:28 PM 14