Recent content by roto25

Homework Statement Prove gcd(lcm(a, b), c) = lcm(gcd(a, c), gcd(b, c)) I've tried coming up with a way to even rewrite it but I'm not really able to do it.

I had just figured out that 1.5 0.5 0.5 1.5 worked out! :)

but if I set x to be 1.1, my matrix would be 1.1 __ __ 1.9 And those two spaces have to be equivalent to 1.1*1.9 - 2, right? because no matter what values I try, when the eigenvalues are getting closer to 1 and two, the matrix is just getting closer to the matrix of: 1 0 0 2

Well, any value of x between 1 and 2 (like 1.1) work.

Yes. Theoretically, I know what it should do. I just can't actually find the right values to do it.

Yeah, I didn't realize that at first. :/

Oh, I had typed 3 instead of 2 for the characteristic polynomial. I ended up looking at this from a Hermitian matrix point of view. And then I got the matrix: 0 i +1 i-1 3 And I did get the right eigenvalues from that. Does that work?

How would you prove, using the integral product, that the set of {cos x, cos 2x, cos 3x, cos 4x, ...} is an orthogonal set?

thanks though!

Does that count for the entries being positive though?

Homework Statement Come up with a 2 x 2 matrix with 2 and 1 as the eigenvalues. All the entries must be positive. Then, find a 3 x 3 matrix with 1, 2, 3 as eigenvalues. The Attempt at a Solution I found the characteristic equation for the 2x2 would be λ2 - 3λ + 2 = 0. But then I couldn't get...