Question

Give the general solution of the equation Ax = b in standard form. a = [...

Give the general solution of the equation Ax = b in standard form.

a = [ 2 1 -1 ] b= [ 3 ]

[ 1 2 1 ] [0 ]

[-1 1 2 ] [-3 ]

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Homework Answers

Answer #1

system is

augmented matrix is

2 1 -1 3
1 2 1 0
-1 1 2 -3

convert into Reduced Row Eschelon Form...

Divide row1 by 2

1 1/2 -1/2 3/2
1 2 1 0
-1 1 2 -3


Add (-1 * row1) to row2

1 1/2 -1/2 3/2
0 3/2 3/2 -3/2
-1 1 2 -3


Add (1 * row1) to row3

1 1/2 -1/2 3/2
0 3/2 3/2 -3/2
0 3/2 3/2 -3/2


Divide row2 by 3/2

1 1/2 -1/2 3/2
0 1 1 -1
0 3/2 3/2 -3/2


Add (-3/2 * row2) to row3

1 1/2 -1/2 3/2
0 1 1 -1
0 0 0 0


Add (-1/2 * row2) to row1

1 0 -1 2
0 1 1 -1
0 0 0 0

reduced system is

...............free variable

general solution is

0 0
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