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 ] = [ y ] [5x + 4y] [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 = = 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 = y y = 5 – 4x

#1 work 2x = (5 – 4x) 2x = – 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.