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...
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...
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) =...
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
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...