If A= diag(a b c) , show that A n = diag(an bn cn) for all positive integers n. Share with your friends Share 1 Manbar Singh answered this We shall prove it by mathematical induction.For n=1, we have,A1 = diaga1b1c1 = diagabc= ASo, the result is true for n=1Let it be true for n=m, so thatAm = diagambmcm Now, Am+1 = Am . A =diagabc . diagambmcm=a000b000c . am000bm000cm=am+1000bm+1000cm+1 = diagam+1bm+1cm+1 So, the result is true for n= m+1, whenever it is true for n=m.Hence, by the principle of mathematical induction, the result is true for all n∈N. 8 View Full Answer Chetna answered this do it by mathematical induction. let P(n)= An= diag(anbncn) -(1) P(1)= A= diag(abc) P(k)=Ak similarly for P(k+1) proving we can say (1) is true by principle of mathematical induction. -4
