Question

given that a= [5 7 3 1 5 2 3 2 1 ]and a^a3-ka2+la=i then

Answer 1

Given : $A = \left[\begin{array}{ccc}5&7&3\\1&5&2\\3&2&1\end{array}\right]$

A³ - kA² + LA  = I

To FInd : k + L

Solution:

$A = \left[\begin{array}{ccc}5&7&3\\1&5&2\\3&2&1\end{array}\right]$

$A^2 = \left[\begin{array}{ccc}41&76&32\\16&36&15\\20&33&14\end{array}\right]$

$A^3 = \left[\begin{array}{ccc}377&731&307\\161&322&135\\175&333&140\end{array}\right]$

$I = \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

377 - k41  + L5  = 1  => 41k - 5L   = 376   => 287k - 35L = 2632

731 - 76k + L7  = 0 =>  76k - 7L  =  731  =>  380k - 35L  = 3655

=> 93k = 1023

=> k = 11

=> L= 15

k + l = 11 + 15 = 26

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