Linear algebra question?

- anonymous

Linear algebra question?

- jamiebookeater

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- anonymous

##### 1 Attachment

- anonymous

Anyone want to help me get started? I am pretty sure I can do the rest on my own.

- anonymous

Represent the system in matrix form

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- anonymous

Yep, that's what I did.

- anonymous

- anonymous

How do I go on from there?

- anonymous

- anonymous

- sirm3d

take the determinant of the coefficient matrix, and set it equal to zero.

- anonymous

Woah woah!!! We haven't learned what a determinant is yet. :P .

- sirm3d

okay.
how about gauss-jordan reduction?

- anonymous

Yeah. We learned that.

- sirm3d

i got something easier than gauss-jordan.
multiply equation 2 by (-1), and equation 3 by 2, then add the two equations.

- anonymous

Elimination?

- sirm3d

yup.

- anonymous

3y-3z=-a+2 ?

- sirm3d

not 3y+3z = -a + 2 ?

- anonymous

Yeah. My mistake.

- anonymous

Allright, what next?

- sirm3d

use that equation with equation 1 to eliminate both y and z.

- anonymous

1 sec.

- anonymous

THat dosen't eliminate it. It makes it bigger.

- sirm3d

bx + 3y + 3z = a
3y + 3z = 2 - a
subtract.

- anonymous

I used substitution instead. Should till be valid right?

- sirm3d

or if you wish to substitute...

- sirm3d

that's valid too.

- sirm3d

bx + (2-a) =a
bx = 2a - 2

- anonymous

|dw:1358650895030:dw|

- sirm3d

you're not to eliminate a, but y and z.

- anonymous

Right.

- anonymous

Lets us elimination then lol.

- anonymous

bx=2a-2?

- sirm3d

yup.

- anonymous

Now would I solve for a and substitute this into equation 2?

- sirm3d

now if you put b = 1, and a any real number other than 1, say 3,
0x = 4
0 = 4 which is clearly false.

- sirm3d

err. i mean put b = 0.

- anonymous

Why can I put 1?

- anonymous

for a*

- anonymous

Ohh never mind. I see why.

- anonymous

For infinitely many solutions I would make 0=0 right?

- sirm3d

right about that.

- anonymous

Okay what about a unique solution? @sirm3d

- sirm3d

unique solution when b is not equal to zero.

- anonymous

and a is 1 right?

- sirm3d

any value of a for as long as b not zero will yield a unique solution

- anonymous

Thanks so much!

- sirm3d

yw.

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