Recent content by ksm100

A^(-1) = [1/det(A)]*adj(A) So I can just say that because I know that det(A) isn't zero, 1/det(A) is defined and therefore A^(-1) exists?

Homework Statement Given that A is any 2x2 matrix show that it is invertible if and only if det(A) \neq 0. Homework Equations The Attempt at a Solution If A is invertible then we know there exists an inverse matrix, say B, such that AB = BA = I. It follows that...

Homework Statement Determine if a limit exists or if the sequence diverges properly. Justify your answer: the sequence is x_n = 2^n/n! Homework Equations From the definition of a limit, I know that I have to prove that for every epsilon (=E) greater than zero, there exists N...

Thank you for your help Galadirith.. I can follow everything that you've done to come up with the last expression that you gave, but then I don't see how that implies that (i) is true.. maybe there's something obvious I'm just not seeing..? Again, thanks for your reply

Homework Statement show by induction that ((1/2)*(3/4)*(5/6)*...*(2n-1)/(2n))^2 is less than/equal to (1/(3n+1)) for n=1, 2, ... The Attempt at a Solution For n=1, (1/2)^2 less than/equal to 1/4 is true (1/4=1/4), so the statement holds for n=1. Assume the statement is true for n...