Download Matrices - Katie Montella

4.1 An Introduction to Matrices
Katie Montella
Mod. 6
5/25/07
Matrices
• A matrix is just a rectangular array of
numbers.
• Now you need to know about rows and
columns.
Rows and Columns
• Rows go this way 
• Columns go this way 
Sample Problem
[ 5x ]
[5x + 4y]
=
[y]
[10]
You want to solve for x and y
Since the matrices are equal, the corresponding
elements are equal.
5x = y
5x + 4y = 10
Sample Problem
The first equation gives a value for y that can be substituted
into the second equation to find the value of x.
5x + 4y = 10
5x + 4(5x) = 10
5x + 20x = 10
25 = 10x
x = 2/5
Sample Problem
To find the value of y, substitute 2/5 into either equation.
5x = y
5(2/5) = y
2=y
The solution is (2/5 , 2).
Practice Problems
• 1.)
[2x] = [40 + 2y]
[ y ] = [ 5 – 4x ]
Try to solve this problem by yourself.
#1 work
• 2x = 40 + 2y
y = 5 – 4x
#1 work
•
•
•
•
•
•
2x = 40 + 2(5 – 4x)
2x = 40 + 10 – 8x
2x = 50 – 8x
2x + 8x = 50
10x = 50
x=5
# 1 Work
•
•
•
•
•
y = 5 – 4x
y = 5 – 4(5)
y = 5 – 20
y = -15
Solution is (5, -15).
Practice Problems
• 2.) [ 2x ] = [ y ]
[2x + 3y] = [12]
• Try to solve this by yourself.
#2 Work
• 2x = y
2x+ 3y = 12
# 2 Work
•
•
•
•
2x +3(2x) = 12
2x + 6x = 12
8x = 12
x =1.5
# 2 Work
•
•
•
•
2x = y
2(1.5) = y
3=y
The solution is (1.5, 3).
The End.
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