Let A 47 5 51 5 35 27 7 2 12 2 12 2 35 6 35 3 19 19 11 2 9

Let A = (47 5 -51 -5 -35 -27 7 -2 -12 -2 -12 -2 35 6 -35 3 -19 -19 11 2 -9 -4 0 -4 -13 -2 11 -4 3 7 7 1 -6 2 -7 -9) Use Mathematical to: i. verify that A^5 notequalto 0 and A^6 = 0, ii. compute the sum sigma^6_j=0 A^j,

Solution

MATLAB CODE for SOLUTION

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% INPUT MATRIX A

A=[47 7 35 11 -13 7; 5 -2 6 2 -2 1; -51 -12 -35 -9 11 -6; -5 -2 3 -4 -4 2; -35 -12 -19 0 3 -7; -27 -2 -19 -4 7 -9];

A5=A^5 % A5 is not zero

A6=A^6 % A6 has all elements 0

% Computing desired sum
S=A^0;
for i=1:6
S=S+A^i;
end

I=eye(6);

I_A=I-A % Finding given matrix I-A

S1=inv(I_A)

S

DIFF=S1-S % Has all values close to zero

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