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Mathematics 64 Online
OpenStudy (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

OpenStudy (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...

OpenStudy (anonymous):

linearly* independent...

OpenStudy (anonymous):

Okay, but how do you get the t-value?

OpenStudy (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)...

OpenStudy (anonymous):

oh, do you mean the t in front of the x1 at r2,c1?

OpenStudy (anonymous):

There are actually two t's the other one at r3,c3

OpenStudy (anonymous):

(I'm in the same class so we're learning about this, so I'm curious as to how to solve this too).

OpenStudy (anonymous):

ok, sorry, misread it...

OpenStudy (anonymous):

I know t = -4 or 3 from the back of the book

OpenStudy (anonymous):

ok, i may nead a second...if that's ok...

OpenStudy (anonymous):

take your time

OpenStudy (anonymous):

is this your first semester of linear algebra?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

ok...

OpenStudy (anonymous):

Mine too

OpenStudy (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 \[t(1+t)-12\neq0\]

OpenStudy (anonymous):

so that is a row in your matrix?

OpenStudy (anonymous):

yes one row ended up to be [0 0 t(1+t)-12| 0]

OpenStudy (anonymous):

ok perfect, thank you!

OpenStudy (anonymous):

Happy to help ^^

OpenStudy (anonymous):

Cool! I actually got that once I pulled out my whiteboard and tried to do row echelon form. Thanks guys!

OpenStudy (anonymous):

Hey quantish you should post more linear algebra problems so it forces me to study. :D

OpenStudy (anonymous):

Haha, you should talk to applekiwi...the solution that I was working on was more backward and difficult ; )

OpenStudy (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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