- #1

Ascendant0

- 132

- 29

- Homework Statement
- -

- Relevant Equations
- -

I didn't have any good way to put this in the homework statement, but this is what the question is asking:

For what c-value(s) will there be a non-trivial solution:

## x_1 - x_2 + x_3 = 0 ##

## 2x_1 + x_2 + x_3 = 0 ##

##-x_1 + (c)x_2 + 2x_3 = 0 ##

I have spent a good couple hours looking at various ways to find non-trivial solutions, but I couldn't find one with a variable like "c" in it. I figured out how to solve without a variable like "c" in them, but not sure what to do with this one.

I tried following the methods in other non-trivial solution videos. I tried to get each line to have the "1s" diagonally down to the right, and put c in the center, but this is the best I've gotten to as far as that:

## [

M=

\left[ {\begin{array}{cc}

1 & -1 & 1 \\

-1 & c & 2 \\

0 & 3 & 1 \\

\end{array} } \right]

] ##

From here, I wasn't seeing any way to clear anything else out without either using fractions, or by including "c" with one of the other equations, which I feel is going to get real sloppy. I know it has to be something simpler than that considering the answer to the problem is ## c = -8 ##. I just can't figure out how to get there. Help would be greatly appreciated.

For what c-value(s) will there be a non-trivial solution:

## x_1 - x_2 + x_3 = 0 ##

## 2x_1 + x_2 + x_3 = 0 ##

##-x_1 + (c)x_2 + 2x_3 = 0 ##

I have spent a good couple hours looking at various ways to find non-trivial solutions, but I couldn't find one with a variable like "c" in it. I figured out how to solve without a variable like "c" in them, but not sure what to do with this one.

I tried following the methods in other non-trivial solution videos. I tried to get each line to have the "1s" diagonally down to the right, and put c in the center, but this is the best I've gotten to as far as that:

## [

M=

\left[ {\begin{array}{cc}

1 & -1 & 1 \\

-1 & c & 2 \\

0 & 3 & 1 \\

\end{array} } \right]

] ##

From here, I wasn't seeing any way to clear anything else out without either using fractions, or by including "c" with one of the other equations, which I feel is going to get real sloppy. I know it has to be something simpler than that considering the answer to the problem is ## c = -8 ##. I just can't figure out how to get there. Help would be greatly appreciated.