Elementary Linear Algebra by Larson, Edwards, and Falvo (5th Edition) 

Problem #79 in Section 1.1 

Solve   x - 4y = -3 using Gaussian elimination, then graph the lines obtained during each step. 

        5x - 6y = 13 

>	# Clear memory and include the "plots" package. restart; with(plots):

 

>

# Define the equations "line1" and "line2" # These are implicitly defined equations, # so we must use "implicitplot". # The "display" command will display both # plots simultaneously. We temporarily # suppress the output by using ":" instead of ";". line1 :=   x -4*y = -3; line2 := 5*x -6*y = 13; plot1 := implicitplot(line1,x=-1..7,y=-1..7): plot2 := implicitplot(line2,x=-1..7,y=-1..7,color=blue): step0 := display(plot1,plot2):

 

 

	(1)

 

>	line1 := x -4*y = -3; line2 :=   14*y = 28; plot1 := implicitplot(line1,x=-1..7,y=-1..7): plot2 := implicitplot(line2,x=-1..7,y=-1..7,color=blue): step1 := display(plot1,plot2):

 

 

	(2)

 

>	line1 := x -4*y = -3; line2 :=      y =  2; plot1 := implicitplot(line1,x=-1..7,y=-1..7): plot2 := implicitplot(line2,x=-1..7,y=-1..7,color=blue): step2 := display(plot1,plot2):

 

 

	(3)

 

>	line1 := x    = 5; line2 :=    y = 2; plot1 := implicitplot(line1,x=-1..7,y=-1..7): plot2 := implicitplot(line2,x=-1..7,y=-1..7,color=blue): step3 := display(plot1,plot2):

 

 

	(4)

 

>	display(step0); display(step1); display(step2); display(step3);

 

>	# Click on the picture below and use the # "animation toolbar" above to play the # animation (You may want to slow the # "frames per second" down from 10 to 1). display([step0,step1,step2,step3], insequence = true);