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