Question

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

Answer 1

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...

Answer 2

linearly* independent...

Answer 3

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

Answer 4

there are no t-values, this is not a dependent system, it is inconssistent, the only solution is the trivial solution (0,0,0)...

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

ok, sorry, misread it...

Answer 9

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

Answer 10

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

Answer 11

take your time

Answer 12

is this your first semester of linear algebra?

Answer 13

yes

Answer 14

ok...

Answer 15

Mine too

Answer 16

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

Answer 17

so that is a row in your matrix?

Answer 18

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

Answer 19

ok perfect, thank you!

Answer 20

Happy to help ^^

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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.