Recent content by morsel

Okay. So the IQR tells the variation of the middle fifty percent of the data, but the sd is less reliable if there are outliers. Does this mean that the IQR and sd don't have a relationship, since sd is not resistant? Would both cases be possible, then?

Homework Statement There are 10 observations. (a) Suppose the IQR is 8. Is it possible that the standard deviation is 1? (b) Suppose the standard deviation is 8. Is it possible that the IQR is 1? Homework Equations IQR = R3 - R1 The Attempt at a Solution My argument is that (a)...

Homework Statement Consider a linear system dx/dt = Ax of arbitrary size. Suppose x1(t) and x2(t) are solutions of the system. Is the sum x(t) = x1(t) + x2(t) a solution as well? How do you know? Homework Equations The Attempt at a Solution I have no idea how to go about this...

Okay. Thank you so much for working through this with me!

Using the Gram-Schmidt process, I get [-1/2 -1/2 1] as the unnormalized second vector. So am I allowed to multiply this by 2 and normalize that to get the second vector in the orthonormal basis?

Where did you get [-1 1 2]? Why can't 1/sqrt(2)[-1 0 1] be a vector in the orthonormal basis?

Okay, so if I normalize [-1 1 0], I get 1/sqrt(2)[-1 1 0] which is what the examples indicate. However, if I normalize [-1 0 1], I get 1/sqrt(2)[-1 0 1], which doesn't match the example. I don't get how they got 1/sqrt(6)[-1 -1 2] from [-1 0 1].

The examples state that the normalization has been done through Gram-Schmidt but I don't get the same results when I try to normalize them with Gram-Schmidt. Is there another way of normalizing?

Homework Statement Example 3 in this pdf: http://karin.fq.uh.cu/qct/Tema_04/04.03.Los%20valores%20y%20vectores%20propios%20de%20un%20sistema/Diagonalization.pdf" Homework Equations Gram-schmidt process: v2 perp = v2 - (u1*v2)u1 The Attempt at a Solution I don't understand how they...

Yes, I know that there's an infinite number of answers but I was wondering whether there was a structured method for finding one. Thank you for your explanation!

Homework Statement Find a 2x2 matrix A for which E1 = span [ 2 1 ] (vertical matrix) is the only eigenspace. Homework Equations The Attempt at a Solution I don't know how to begin this problem.. Any hints?

Does it go back to the original point?

Homework Statement Let A be the matrix of an orthogonal projection. Find A^2 in two ways: a. Geometrically. (consider what happens when you apply an orthogonal projection twice) b. By computation, using the formula: matrix of orthogonal projection onto V = QQ^T, where Q = [u1 ... um]...

Homework Statement Note: the vectors are column vectors, not row vectors. Latex is not working for me right now. Find an orthonormal basis u1, u2, u3 of R3 such that span(u1) = span [1 2 3] and span(u1,u2) = span { [1 2 3], [1 1 -1] } Homework Equations The Attempt at...

Thanks for your help. I understand how to approach the other problems but I'm still unsure about #4. Is the dimension n-1 because there's a free variable? In other words, n-1 number of leading 1's in the rref form?