Thread: More Gauss-Jordan help please?

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

2x + 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 ]

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.
.
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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.

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?

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 .