Recent content by paulrb

Thanks for your help, it allowed me to finish the rest of the proof.

Homework Statement Let S be a subset of a vector space V, and let v be an element of V. Show that span(S) = span(S U {v}) if and only if v is an element of span(S) Homework Equations The Attempt at a Solution I'm honestly not sure how to get started, I've spent time looking...

Homework Statement Find a spanning set for the space of all 3x3 symmetric matrices. Homework Equations The Attempt at a Solution I know how to find the spanning set for vectors, but I don't know if it works the same way for matrices. Is the set's elements matrices? If so, would...

Homework Statement Prove that the set of all 3-vectors orthogonal to [1, -1, 4] forms a subspace of R^3. Homework Equations Orthogonal means dot product is 0. The Attempt at a Solution I know the vectors in this subspace are of the form [a,b,c] where a - b + 4c = 0. However I...

Homework Statement Let A and B be n x n matrices. Show that if AB = -BA and n is odd, then A or B is singular. Homework Equations - A matrix is singular iff its determinant is 0. or possibly: Theorem: if A and B are both n x n matrices, then |AB| = |A||B| The Attempt at a Solution...

Homework Statement Suppose that AX = O is a homogeneous system of n equations in n variables. If the system (A^2)X = O has a nontrivial solution, show that AX = O has a nontrivial solution. Homework Equations Reduced row echelon form definition, matrix multiplication, etc. The...

Edit: Sorry, I figured this out shortly after posting. It's a simple problem but I hadn't used matrix equations before. Homework Statement If A, B, and C are all square matrices of the same size, show that AB commutes with C if A and B both commute with C. Homework Equations Formula for...

Thank you, that was enough for me to figure it out :)

Homework Statement Let x and y be nonzero vectors in Rn. Prove ||x+y|| = ||x|| + ||y|| if and only if y = cx for some c > 0. Homework Equations Formula for vector magnitude, basic properties of vectors, possibly other vector formulas The Attempt at a Solution I have proved the...

I worked on it a bit more and figured everything out. Thanks for your help.

Ok...put the points for y won't be numbers, but variables. if x = 0, y = -(c/b) giving point (0, -c/b) if x = 1, y = (-c-a)/b giving point (1, -c/b - a/b) Now I have a vector: [1, -a/b] using y = 0 and y = 1 for the second equation will give me [a/b, 1] These are orthogonal! Thank you! Now...

Sorry, I didn't have time to actually do the problem before. Now that I'm looking at it again, I'm still confused. How do I relate the first equation to the second equation? For example, if I choose x=0 y=0 for the first equation, what do I do with that? I get c = 0, but that doesn't tell me...

Thank you, I'm not sure why I didn't think of it like that before...

Homework Statement Show that the lines given by the equation ax + by + c = 0 and bx - ay + d = 0 (where a, b, c, d are in R) are perpendicular by finding a vector in the direction of each line and showing that these vectors are orthogonal. (Hint: Watch out for the cases in which a or b equals...

Thank you, that really clears a lot up for me. But just to clarify: is the reverse of that true as well? - If you cross a junction no matter which side you choose, the capacitors/resistors/etc. must be in parallel.