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First find the general solution to the differential equation y'' + 4y' + 3y = 0 as an arbitrary number of the solution to this differential equation can be added to the solution of the differential equati...

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...