Answer the following questions.If `A=[[3,-4],[1,-1]]`,prove that `A^n=[[1+2n,-4n],[n,1-2n]]`for all `n in N`

Answer the following questions.If A=[[costheta,sintheta],[-sintheta,costheta]] ,prove that A^n=[[cos ntheta,sin ntheta],[-sin ntheta,cos ntheta]] , for all n in N

Prove by method of induction: P(n) = [[3,-4],[1,-1]]^n = [[2n+1, -4n],[n, -2n+1]]

By method of induction, prove that 2^n > n , for all n in N .

By method of induction, prove that 1.6 + 2.9 + 3.12 +... +to n terms = n(n +1 )(n+2) for all n in N .

Prove the following by the method of induction for all n in N : Prove by methode of Induction [[1,2],[0,1]]^n = [[1,2n],[0,1]] AA n in N

Choose the correct alternative answer for each of the following questions : M = {1, 3, 5}, N = {2, 4, 6,}, then M nn N =?

Choose the correct alternative answer for each of the following questions : M uu N = {1, 2, 3, 4, 5, 6} and M = {1, 2, 4} then which of the following represent set N?

By method of induction prove that 1.3 + 2.5 + 3.7 +...+ n (2n + 1) = n/6 (n + 1) (4n + 5) for all n in N