Find a 3x1 matrix x, with entries not all zero such that Ax = x

Given the matrix , I've to find a vector x, such that Ax = x.

I'm not quite sure what's the best way of solving a question like this, I can try some values that could be correct, doing some half educated guesses, but that just seems clumsy and slow. Any tips?

Re: Find a 3x1 matrix x, with entries not all zero such that Ax = x

If then,

Solving the linear system, we obtain all the solutions. For example, is a non zero solution.

Re: Find a 3x1 matrix x, with entries not all zero such that Ax = x

I think I still don't understand right, if Ax=x, then if x = (3, 1, -2), then:

What am I missing here? Why do you let the equations be 0? According to my textbook the answer (a answer?) should be . I see how this is a solution:

I know how to solve a system of equations, but I don't get this...

Re: Find a 3x1 matrix x, with entries not all zero such that Ax = x

Quote:

Originally Posted by

**Lepzed** What am I missing here?

, and you have written .

Re: Find a 3x1 matrix x, with entries not all zero such that Ax = x

Ah, that was a typo, it should indeed be '2', not '-2', my apologies for that. But still, how did you get to your answer? Why did you let the equations be 0?

Re: Find a 3x1 matrix x, with entries not all zero such that Ax = x

With your reformulation

http://quicklatex.com/cache3/ql_d98c...e897bd0_l3.png

and a non null solution is .

Re: Find a 3x1 matrix x, with entries not all zero such that Ax = x

Ah, so basically you subtracted an x_row from each row, to make the equation 0 and than you just fill in the blanks?