Download Warm-Up - Walton High

Warm-Up - 8/30/2010
Simplify.
1.) 12    5   4 
multiply
2.) 3  9  28
3.)  3   9   28
4.) 7  8 
5.) 2  4  7  12
Agenda
8/30/2010
Tue Aug 31
• Warm-Up
• Notes Perform Basic
Matrix Operations
• Practice
Multiply
Matrices
WEB Sept 1
Multiply
Matrices
Thu Sept 2
You MUST have a
GRAPHING
CALCULATOR for this
unit.
Review
Fri Sept 3
Quiz
NON - CALCULATOR
1.8
Perform Basic
Matrix Operations
Page 38
Matrix (matrices)
Column 1 Column 2 Column 3 Column 4
 a11 a12 a13 a14 

a
a22 a23 a24 
Row 2  21
a32 a33 a34 
Row 3  a31





Row m 
 amn amn amn amn 
Row 1
Row, Row, Row then Column
That’s the Matrix way
Entries, Dimensions, Multiplication
It’s row then the column!
A matrix of m rows and n columns is called a
matrix with dimensions m x n.
Ex. Find the dimensions.
 2 3 4 


 1 1  

2

2 X 3
10 
 7  2 X 1
 
3



 6
8
2
7
3 X 3
 3
4
1 X 2
9

5
8 
To add matrices, we add the corresponding
elements. They must have the same
dimensions.
5 0
A

 4 1
6 3
B

2 3 
 5  6 0  3
A+B 

 4  2 1 3 
 1 3 


6 4 
To subtract matrices, we subtract the
corresponding elements. The matrices must
have the same dimensions.
1
 2

 3
2

0
1

1
1

 2
1

3
3 
 2



1

5
3 
 
Not possible – dimensions don’t match
Scalar Multiplication:
2k 3k 
1 2 3
 1k




k  1 2 3  1k 2k 3k


 4 5 6
 4k 5k 6k 
We multiply each # inside our matrix by k.
 3 0 
3

 4 5
1 2 x 


5 4 y 1 
2
0 5 x 
Multi-Step Problems
Solve the matrix equation for x and y:
 3x 1  4 1   26 0
2 





  8 5  2  y   12 8
Solve the matrix equation for x and y:
 3x  4
0   26
2 


5  y   12
 6
 6 x  8
0    26



10  2 y   12
  12
0

8
0

8
Equate corresponding elements and solve the two resulting
equations
 6 x  8
0    26 0




10  2 y   12 8
  12
6x  8  26
x 3
10  2 y  8
y 1
7 5 
 1 3
 2 8 
 8 4 
B
A


 0 2  D   5 2 
1
0
2
6
C









 3 1
 1 3 
Find C + D
Find C + C
Find 3D + 3C
Find D – A
7 5 
 1 3
 2 8 
 8 4 
B
A


 0 2  D   5 2 
1
0
2
6
C









 3 1
 1 3 
Find A + B
Find A + C
Find 2A + 3B
Find D – B
7 5 
 1 3
 2 8 
 8 4 
B
A


 0 2  D   5 2 
1
0
2
6
C









 3 1
 1 3 
Find ½B
Find -5D
Find B – A
Find D – C