# Search results

1. ### Numerical analysis

Homework Statement Consider the equation y0 = Ly; y(0) = 1: **L = lamda** Verify that the solution to this equation is y(t) = e^(Lt). We want to solve this equation numerically to obtain an approximation to y(1). Consider the two following methods to approximate the solution to this...
2. ### Lagrange, cosets, indicies

Homework Statement suppose that H and K are subgroups of a group G such that K is a proper subgroup of H which is a proper subgroup of G and suppose (H : K) and (G : H) are both finite. Then (G : K) is finite, and (G : K) = (G : H)(H : K). **that is to say that the proof must hold for...
3. ### Open sets

Homework Statement how do you show a set is open in R^n? Homework Equations The Attempt at a Solution
4. ### Closure math problems

Homework Statement 6) Prove or give a counter-example of the following statements (i) (interiorA)(closure) intersect interior(A(closure)): (ii) interior(A(closure)) intersect (interiorA(closure)): (iii) interior(A union B) = interiorA union interiorB: (iv) interior(A intersect B) =...
5. ### First isomorphism theorem

Homework Statement can someone explain the 1st isomorphism theorem to me(in simple words) i really dont get it Homework Equations The Attempt at a Solution
6. ### Homomorphism help

Homework Statement let R* be the group of nonzero real numbers under multiplication. then the determinant mapping A-> det(A) is a homomorphism from GL(2,R) to R*. the kernel of the determinant mapping is SL(2,R). i am suppose to show that this is a homomorphism but i have no idea where to...