Dido525
Linear algebra question?



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Dido525
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Dido525
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Anyone want to help me get started? I am pretty sure I can do the rest on my own.

Cecily
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Represent the system in matrix form

Dido525
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Yep, that's what I did.

Dido525
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@Cecily

Dido525
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How do I go on from there?

Dido525
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@zepdrix @Outkast3r09

Dido525
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@dumbcow

sirm3d
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take the determinant of the coefficient matrix, and set it equal to zero.

Dido525
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Woah woah!!! We haven't learned what a determinant is yet. :P .

sirm3d
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okay.
how about gaussjordan reduction?

Dido525
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Yeah. We learned that.

sirm3d
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i got something easier than gaussjordan.
multiply equation 2 by (1), and equation 3 by 2, then add the two equations.

Dido525
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Elimination?

sirm3d
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yup.

Dido525
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3y3z=a+2 ?

sirm3d
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not 3y+3z = a + 2 ?

Dido525
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Yeah. My mistake.

Dido525
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Allright, what next?

sirm3d
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use that equation with equation 1 to eliminate both y and z.

Dido525
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1 sec.

Dido525
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THat dosen't eliminate it. It makes it bigger.

sirm3d
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bx + 3y + 3z = a
3y + 3z = 2  a
subtract.

Dido525
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I used substitution instead. Should till be valid right?

sirm3d
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or if you wish to substitute...

sirm3d
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that's valid too.

sirm3d
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bx + (2a) =a
bx = 2a  2

Dido525
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dw:1358650895030:dw

sirm3d
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you're not to eliminate a, but y and z.

Dido525
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Right.

Dido525
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Lets us elimination then lol.

Dido525
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bx=2a2?

sirm3d
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yup.

Dido525
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Now would I solve for a and substitute this into equation 2?

sirm3d
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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
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err. i mean put b = 0.

Dido525
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Why can I put 1?

Dido525
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for a*

Dido525
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Ohh never mind. I see why.

Dido525
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For infinitely many solutions I would make 0=0 right?

sirm3d
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right about that.

Dido525
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Okay what about a unique solution? @sirm3d

sirm3d
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unique solution when b is not equal to zero.

Dido525
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and a is 1 right?

sirm3d
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any value of a for as long as b not zero will yield a unique solution

Dido525
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Thanks so much!

sirm3d
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yw.