Recent content by bluewhistled

[L-1 -3 0 -3 L-1 0 0 0 L+2] (L+2)((L-1)^2 - 9) (L+2)(L^2 -2L +1 -9) (L+2)(L^2 -2L -8) (L^3 -2L^2 -8L +2L^2 -4L -16) L^3 -12L -16 ... meh, got it nevermind. Thanks for the suggestion.

Homework Statement a matrix A: [1 3 0 3 1 0 0 0 -2] Find Q and D where QTAQ=D The Attempt at a Solution I found the eigenvalues of -4,2,2 When I plug them back in and rref the matrix I only get the trivial solution meaning the matrices are linearly independent. How do I get...

Also a book I found claims that the null space IS the perp complement of the row space. And when I do a dot product of each of the null space vectors I found against the original they add up to 0.

I guess I just don't understand the latex code. The cryptic mathematical way of keeping things short and sweet. If you don't mind, could you explain how to get it in a much more detailed method? I'm rather slow with this stuff.

Are what I have found incorrect? Are the nullspace of this solution not the basis for w perp? Because when I test it it comes out correct. But once again it's only the basis for w perp. NOT w perp itself.

Yes and I got the two free variables, and then from there, which I think I got the general solution for. But I don't understand what you mean from there.

So my solution is incorrect? And if I do that, and I find w perp's basis. I'm not finding w perp.

I essentially answered my question before. My first one was getting convoluted with my posts. So I started a new one based on a different question. Would you mind deleting my original thread? And if you do, would you mind deleting your post claiming I started multiple threads so as not to...

Homework Statement I don't understand the difference between an orthogonal complement and it's basis. In this problem: W = [x,y,z]: 2x-y+3z=0 Find w's orthogonal complement and the basis for the orthogonal complement. The Attempt at a Solution I did a quick reduced row echelon to [2,-1,3]...

So I mean.. If that's right, then what is the complement and what is the basis? Argh I feel like nothing will give me a straight answer. Could someone explain what it is that's going on here? I'd truly appreciate it.

or.. x_1 + -.5x_2 +1.5x_3 = 0 and then x_1 = .5x_2 - 1.5x_3 which means that [.5,1,0] and [-1.5,0,1] are the nullspaces which are also the complements?

Okay.. I'm reading that the perp is the nullspace of the matrix. [2,-1,3], reduce row echelon form it to [1,-.5,1.5]. which is just x-.5y+1.5z=0 now I know that isn't right.

Homework Statement W=[x,y,z]: 2x-y+3z=0 find W perp and give a basis for W perp The Attempt at a Solution None, I have no idea how to do this. No lecture on it, no textbook, and can't find anything on the net ;\ If someone could point me in the right direction I'd really appreciate it.

Nm, I figured it out. when looking for the eigenvector for 3 it actually splits into 2. I think I did the math wrong the first time. Thanks you guys.

Can one of you help me find the generalized vectors I have no idea what to do.