Question

if A=[aij]such that aij=(i+j)² then find trace of A pls answer it fast​

Answer 1

Answer's in the pic.

Answer 2

Given : A=[aij]such that aij=(i+j)²

To Find :  trace of A

Solution:

aij=(i+j)²  

All diagonal elements from upper left to lower right would be :

a11  = ( 1 + 1)²  = 2² = 2²×1²

a22 = (2 + 2)² = 4² = 2²×2²

ann = (n+n)² = (2n)² = 2²n²

trace of A = Sum of diagonal elements from  

= 2²×1² + 2²×2² + 2²n²

= 2² ( 1² + 2² + .........................+ n²)

= 2² ( n)(n + 1)(2n + 1) /6

= 2 ( n)(n + 1)(2n + 1) /3

trace of A = 2 ( n)(n + 1)(2n + 1) /3

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