Recent content by Luxe

I am in a class where we are studying concepts and design of programming languages. For a project we are suppose to design our own programming language or come up with some alternative project idea to do for the class. So, my question is... do ya'll have any ideas for an interesting and...

Homework Statement Linear Algebra: For all the unit vectors u=[x,y,z]^T in R^3. Find the one for which the sum x+8y+2z is minimal. (u is a 3 x 1 vector) Homework Equations The Attempt at a Solution I tried working this with the least squares method...it wasn't right. I am...

Homework Statement A particle with charge 2.8 C moves through a uniform magnetic field. At one instant the velocity of the particle is (1.4 i + 1.2 j + 0.48 k) m/s and the magnetic force on the particle is (11.9 i - 14.1 j + 1.57 k) N. The x and y components of the magnetic field are equal...

I still have no idea on the last one. I have looked all through my book...

ok, i think that for 2 implies 3. A being nonsingular says that A inverse exists. So, then you can show that x= (inverseA)*B which proves #3. Is this right? Now, the one I am stuck on is 3 implies 1. Any hints to get me started?

Ok I think I figured the first part out: The columns of A are linearly independent. So, A is row equivalent to the identity matrix, and Ax=0 and Ix=0 have only the solution, x=0. So, the A=E1E2...Ek, which says that the product of invertiable matrices is invertiable and E is invertiable, so A...

if N(A)=0 then in the equation Ax=0, x equals 0. But then how do you show that A is invertible from that?

Homework Statement Prove that the following are equivalent: 1. N(A)=0 2. A is nonsingular 3. Ax=b has a unique solution for each b that exists in R^n. Homework Equations The Attempt at a Solution I think you prove this by showing that 1 implies 2, 2 implies 3, & 3 implies 1...

Homework Statement Let A and B be n x n matrices and let C= A - B. Show that if Ax=Bx, and x does not equal zero, then C must be singular. Homework Equations The Attempt at a Solution Ax-Bx=0 x(A-B)=0 x(C)=0 So, Cx=0 Does that mean C is singular?

Homework Statement Give a proof: Let C be a square matrix. Show if C^(k+1)=0, then I-C is nonsingular and (I-C)^-1=I+C+C^2+...+C^k. Homework Equations I don't know. I can't find a theorem that will help me. The Attempt at a Solution I know if a matrix is nonsingular, it has an...