if B, C ARE n ROWED SQUARE MATRICES AND IF A=B+C , BC=CB ,C2=0 ,THEN SHOW THAT FOR EVERY n - Maths - Matrices

Question

if B, C ARE n ROWED SQUARE MATRICES AND IF A=B+C , BC=CB
,C2=0 ,THEN SHOW THAT FOR EVERY n is the element ofN, A
n+1 =Bn(B+(n+1)C)

Himanshu · Accepted Answer

Let P(n) be the statement given by

For n = 1, we have

Hence, the statement is true for n = 1 Assume that the statement is true for n = k

We shall now show that P(k + 1) is true That is we need to show that

Now,

So, the statement is true for n = k + 1 Thus, P(k) is true ÃžP(k + 1) is true Hence, by the principle of mathematical induction P (n) is true for all n ÃŽN

if B, C ARE n ROWED SQUARE MATRICES AND IF A=B+C , BC=CB ,C2=0 ,THEN SHOW THAT FOR EVERY n is the element ofN, A n+1 =Bn(B+(n+1)C).

if B, C ARE n ROWED SQUARE MATRICES AND IF A=B+C , BC=CB ,C²=0 ,THEN SHOW THAT FOR EVERY n is the element ofN, Aⁿ⁺¹ =Bⁿ(B+(n+1)C).