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In order to do this we must follow the standard procedure for a proof by induction which is to first check a base case:Let n = 1, then the sum can be written as 1² = 1/6(1+1)(2+1) = 1 as requir...

We must show that the set satisfies the group requirements: Identity, Closure, Associativity and Invertibility.Identity: Contains identity matrixAssociativity: Follows from the rules of matrix multiplicat...

Note the simplest relation to eliminate t is the fact cos²(t)+sin²(t)=1 for all t, so we need only find x and y in terms of cos(t) and sin(t).Note we have sin(t)=-(y+1) from the equa...

We are given M = [[-2,6],[1,3]], with columns [-2,6] and [1,3]. To find P and D, eigenvalues and eigenvectors must be calculated, as D is defined to be the matrix whose diagonal is comprised of the eigenv...

Have a picture of full working with annotation to go through during interview.Here is rough outline:y = cosh^-1(x)x = cosh(y)x = (e^y+e^-y)/22x = e^y+e^-y...