matrix

**prasum** · August 31st 2011, 05:13 PM

let A=[aij],where aij=uivj 1<=i<=n and 1<=j<=n and ui,vj belong to R satisfies A^5=16A find trace(A)

**FernandoRevilla** · August 31st 2011, 07:36 PM

Hint: Denoting $U=\begin{pmatrix}u_1\\ \vdots\\{u_n}\end{pmatrix},\;V=\begin{pmatrix}v_1, v_2,\hdots,v_n\end{pmatrix}$ we verify $A=UV$ and $A^5=(u_1v_1+\ldots+u_nv_n)^4A=(\textrm{tr}A)^4A$

**prasum** · September 1st 2011, 05:06 PM

whats the final answer is it 11

**FernandoRevilla** · September 1st 2011, 10:25 PM

Originally Posted by prasum

whats the final answer is it 11

Why?

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