CoCalc -- 4735.sagews

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L=matrix([[0,1,1.5,0,0],[0.9,0,0,0,0],[0,0.8,0,0,0],[0,0,0.7,0,0],[0,0,0,0.5,0]]);L

[0.000000000000000  1.00000000000000  1.50000000000000 0.000000000000000 0.000000000000000]
[0.900000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.800000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.700000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.500000000000000 0.000000000000000]

L^51

[ 426654.326572642  622233.516140712  487582.006288389 0.000000000000000 0.000000000000000]
[ 292549.203773033  426654.326572642  334326.200942009 0.000000000000000 0.000000000000000]
[ 178307.307169072  260043.736687141  203770.192611303 0.000000000000000 0.000000000000000]
[ 95092.7565519412  138683.461131500  108672.323911322 0.000000000000000 0.000000000000000]
[ 36224.1079704405  52829.3091955229  41397.0282441370 0.000000000000000 0.000000000000000]

X=matrix([[10000],[20000],[15000],[10000],[8000]]);X

[10000]
[20000]
[15000]
[10000]
[ 8000]

L^51*X

[2.40249436828665e10]
[1.64734715833133e10]
[1.00405006946031e10]
[ 5.35468164681924e9]
[ 2.03978268727692e9]