• July 15th 2008, 12:19 PM
tuheetuhee
Determine a relationship between the constants
a and b if the system below is to have infinitely many solutions.

x
+ 2y + z = 1 + b

x 2y + z = a + 2b 1

2
x + 4y + 3z = 2b + 2

Okay so this is what I have so far:

[ 1 2 1 | 1+b ]
[-1 -2 1 | a+2b-1]
[ 2 4 3 | 2b +2 ]

.
.
.
.
After ysing the G-J method, I get all the way to
[1 0 3/2 | 1/2a + b]
[0 0 2 | a + 3b ]
[0 0 0 | -2 ]

SO its in row-reduced form now...I think. Feeling a bit stuck at this point.

• July 15th 2008, 06:47 PM
TKHunny
You started with a non-singular matrix. How did it turn singular on you?

Better try that reduction again.

Are you sure you reported the problem correctly?
• July 15th 2008, 07:12 PM
ThePerfectHacker
Quote:

Originally Posted by tuheetuhee
[ 1 2 1 | 1+b ]
[-1 -2 1 | a+2b-1]
[ 2 4 3 | 2b +2 ]

[1 2 1 | 1+b]
[0 0 2 | a+3b]
[2 4 3 | 2b+2]

[1 2 1 | 1+b]
[0 0 2 | a+3b]
[0 0 1 | 0 ]

[1 2 1 | 1+b]
[0 0 0 | a+3b]
[0 0 1 | 0 ]

[1 2 1 | 1+b]
[0 0 1 | 0 ]
[0 0 0 | a+3b]

[1 2 0 | 1+b]
[0 0 1 | 0]
[0 0 0 | a+3b]

To have solutions we require that $a+3b=0$.