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Anyone want to help me get started? I am pretty sure I can do the rest on my own.
Represent the system in matrix form
Yep, that's what I did.
How do I go on from there?
take the determinant of the coefficient matrix, and set it equal to zero.
Woah woah!!! We haven't learned what a determinant is yet. :P .
okay. how about gauss-jordan reduction?
Yeah. We learned that.
i got something easier than gauss-jordan. multiply equation 2 by (-1), and equation 3 by 2, then add the two equations.
not 3y+3z = -a + 2 ?
Yeah. My mistake.
Allright, what next?
use that equation with equation 1 to eliminate both y and z.
THat dosen't eliminate it. It makes it bigger.
bx + 3y + 3z = a 3y + 3z = 2 - a subtract.
I used substitution instead. Should till be valid right?
or if you wish to substitute...
that's valid too.
bx + (2-a) =a bx = 2a - 2
you're not to eliminate a, but y and z.
Lets us elimination then lol.
Now would I solve for a and substitute this into equation 2?
now if you put b = 1, and a any real number other than 1, say 3, 0x = 4 0 = 4 which is clearly false.
err. i mean put b = 0.
Why can I put 1?
Ohh never mind. I see why.
For infinitely many solutions I would make 0=0 right?
right about that.
Okay what about a unique solution? @sirm3d
unique solution when b is not equal to zero.
and a is 1 right?
any value of a for as long as b not zero will yield a unique solution
Thanks so much!