If `A= [[1,0],[1,1]]and I= [[1,0],[0,1]]`, which one of the
following holds for all `n ge1`, (by the principal of
mathematical induction)

If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following holds for all nge1 by the principle of mathematica induction? (A) A^n=2^(n-1) A+(n-1)I (B) A^n=nA+(n-1) I (C) A^n=2^(n-1) A-(n-1)I (D) A^n=nA-(n-1) AI

If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following holds for all nge1 by the principle of mathematica induction? (A) A^n=2^(n-1) A+(n-1)I (B) A^n=nA+(n-1) I (C) A^n=2^(n-1) A-(n-1)I (D) A^n=nA-(n-1) AI

Prove the following by the principle of mathematical induction: 1+3+3^2++3^(n-1)=(3^n-1)/2

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

Prove the following by the principle of mathematical induction: 1/2+1/4+1/8++1/(2^n)=1-1/(2^n)

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

If A= [[1 , 0],[ − 1, 7]] and I=[[1, 0],[ 0 ,1]] , then find k so that A^2=8A+k I

If A=[(0,-1),(1,0)] , then which one of the following statements is not correct ?

Prove the following by the principle of mathematical induction: \ 1. 2+2. 3+3. 4++n(n+1)=(n(n+1)(n+2))/3

Prove the following by using the principle of mathematical induction. n(n+1)+1 is an odd natural number, n in N .