anonymous
  • anonymous
For which values of t does the following homogeneous linear system have non-trivial solutions? 12x1-x2+x3=0 tx1 +x3=0 x2+tx3=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
coefficient matrix = 12, -1, 1; 1,0,1; 0,1,1... augmented matrix = 12,-1, 1,0; 1,0,1,0; 0,1,1,0.... RREF---> gives identity matrix, so they are all liniar independent...
anonymous
  • anonymous
linearly* independent...
anonymous
  • anonymous
Okay, but how do you get the t-value?

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More answers

anonymous
  • anonymous
there are no t-values, this is not a dependent system, it is inconssistent, the only solution is the trivial solution (0,0,0)...
anonymous
  • anonymous
oh, do you mean the t in front of the x1 at r2,c1?
anonymous
  • anonymous
There are actually two t's the other one at r3,c3
anonymous
  • anonymous
(I'm in the same class so we're learning about this, so I'm curious as to how to solve this too).
anonymous
  • anonymous
ok, sorry, misread it...
anonymous
  • anonymous
I know t = -4 or 3 from the back of the book
anonymous
  • anonymous
ok, i may nead a second...if that's ok...
anonymous
  • anonymous
take your time
anonymous
  • anonymous
is this your first semester of linear algebra?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok...
anonymous
  • anonymous
Mine too
anonymous
  • anonymous
You learn how to turn that system into matrix right? It is easier if you did. With that technique you will end up with t(1+t)-12 to get nontrivial solution, that expression must not equal to 0 so you just solve \[t(1+t)-12\neq0\]
anonymous
  • anonymous
so that is a row in your matrix?
anonymous
  • anonymous
yes one row ended up to be [0 0 t(1+t)-12| 0]
anonymous
  • anonymous
ok perfect, thank you!
anonymous
  • anonymous
Happy to help ^^
anonymous
  • anonymous
Cool! I actually got that once I pulled out my whiteboard and tried to do row echelon form. Thanks guys!
anonymous
  • anonymous
Hey quantish you should post more linear algebra problems so it forces me to study. :D
anonymous
  • anonymous
Haha, you should talk to applekiwi...the solution that I was working on was more backward and difficult ; )
anonymous
  • anonymous
I have a test coming up and even though I look over the material in the chapters, make flashcards full of definitions and theorems, and try to pratice and review problems, I am very slow.

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