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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...