Matrices can be so mind blowing

Algebra Level 3

Find the trace of the matrix below.

( 2 1 1 0 1 0 1 1 2 ) 20 \large \begin{pmatrix}{2} && {1} && {1} \\ {0} && {1} && {0} \\ {1} && {1} && {2}\end{pmatrix} ^{20}

4836874430 3486784403 330448678 434486702

Benjamin Ononogbu by Benjamin ononogbu , 24, USA

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1 solution

Otto Bretscher
Oct 9, 2015

The eigenvalues are quickly seen to be 1,1,3 since A − I 3 A-I_3 has rank 1. Thus the trace of A 20 A^{20} is 3 20 + 2 ∗ 1 20 = 3486784403 3^{20}+2*1^{20}=\boxed{3486784403}

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perfect solution

Benjamin ononogbu - 5 years, 8 months ago

pls try my question name "this is just a give away"

Benjamin ononogbu - 5 years, 8 months ago

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