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Let A = [aij] , where aij = uij , 1 ≤ j ≤ n , 1≤ i ≤ n and ui , vj belongs to R satisfies A5 = 16 A , find tr(A).
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11 Answers
6the ans is given simply 2.......
can u tell how did u do it??
i had a doubt
that the matrix \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}
will also satisfy the condn......
so in this case trace is 4...........how can it be only 2??
21''answer can't be simply two''
Lets see [6]:D
tr(A)= \sum_{k=1}^{n}a_{kk}= \sum_{k=1}^{n}(u_kv_k)
Let A^2 = [a"_{ij}]= \sum_{k=1}^{n}(a_{ik}a_{kj})= \sum_{k=1}^{n}(u_iv_ku_kv_j)= u_iv_j\sum_{k=1}^{n}v_ku_k= u_iv_j(tr(A))
Similarly A^5 = [a""_{ij}]= u_iv_j(tr(A))^4
But A^5 = 16A so tr(A)= 2,-2