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inverse of matrix 18x18

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ANAND ASP
ANAND ASP on 28 Nov 2020
Answered: Walter Roberson on 28 Nov 2020
A=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0.960000000000000 0 0 0 0 -0.960000000000000 0 0 0 0 0 0 0 0 0 0 0;
0 0 2.23790608695652 0 0 0 0 0 -1.33550608695652 0 0 0 0 0 0 0 0 0;
-1.24547021739130 0 0 25.4935942611344 -11.6040718529838 -10.5106639714776 0 0 0 0 0 0 3.30740954238180 1.36517736605472 1.94219279132692 0 0 0;
0 0 0 -11.6040718529838 3.59689473818280 0 -5.97512017854242 0 0 0 0 0 1.36517736605472 2.55280007950317 0 1.18760382787156 0 0;
0 0 0 -10.5106639714776 0 2.11657463928156 0 0 -5.58823079251630 0 0 0 1.94219279132692 0 3.22418780554366 0 0 1.28201098652570;
0 -0.960000000000000 0 0 -5.97512017854242 0 6.65075604340637 -13.6979757743444 0 0 0 0 0 1.18760382787156 0 2.80471238660181 1.61711697025140 0;
0 0 0 0 0 0 -13.6979757743444 -5.54012668752085 -9.78425422305323 0 0 0 0 0 0 1.61711697025140 2.77219546898122 1.15508187530801;
0 0 -1.33550608695652 0 0 -5.58823079251630 0 -9.78425422305323 -12.3143655823924 0 0 0 0 0 1.28201098652570 0 1.15508187530801 2.43710327055050;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 -3.30737015738164 1.36517736605472 1.94219279132692 0 0 0 0 0 0 55.5915770671030 -11.6040718529838 -10.5106639714776 0 0 0;
0 0 0 1.36517736605472 -2.55276150142619 0 1.18760382787156 0 0 0 0 0 -11.6040718529838 33.6949232068892 0 -5.97512017854242 0 0;
0 0 0 1.94219279132692 0 -3.22418448881414 0 0 1.28201098652570 0 0 0 -10.5106639714776 0 32.2146426775241 0 0 -5.58823079251630;
0 0 0 0 1.18760382787156 0 -2.80471913975820 1.61711697025140 0 0 0 0 0 -5.97512017854242 0 66.8288576325249 -13.6979757743444 0;
0 0 0 0 0 0 1.61711697025140 -2.77220222213760 1.15508187530801 0 0 0 0 0 0 -13.6979757743444 54.6379749015977 -9.78425422305323;
0 0 0 0 0 1.28201098652570 0 1.15508187530801 -2.43709623841190 0 0 0 0 0 -5.58823079251630 0 -9.78425422305323 79.3225061858399]
its 18x18 matrix, i want to find inverse
i tried with inv(A) but it shows "Warning: Matrix is singular to working precision."
then it shows all elements are "inf"
i want to invert it for further calculation

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Answers (2)

M.Many
M.Many on 28 Nov 2020
The inverse doesn't exist because A is singular, this means that one or more rows are linearly dependent from other rows. A is inversible if and only if det(A) =/= 0. However, the determinant of A is 0 here.

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Walter Roberson
Walter Roberson on 28 Nov 2020
format long g
A=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0.960000000000000 0 0 0 0 -0.960000000000000 0 0 0 0 0 0 0 0 0 0 0;
0 0 2.23790608695652 0 0 0 0 0 -1.33550608695652 0 0 0 0 0 0 0 0 0;
-1.24547021739130 0 0 25.4935942611344 -11.6040718529838 -10.5106639714776 0 0 0 0 0 0 3.30740954238180 1.36517736605472 1.94219279132692 0 0 0;
0 0 0 -11.6040718529838 3.59689473818280 0 -5.97512017854242 0 0 0 0 0 1.36517736605472 2.55280007950317 0 1.18760382787156 0 0;
0 0 0 -10.5106639714776 0 2.11657463928156 0 0 -5.58823079251630 0 0 0 1.94219279132692 0 3.22418780554366 0 0 1.28201098652570;
0 -0.960000000000000 0 0 -5.97512017854242 0 6.65075604340637 -13.6979757743444 0 0 0 0 0 1.18760382787156 0 2.80471238660181 1.61711697025140 0;
0 0 0 0 0 0 -13.6979757743444 -5.54012668752085 -9.78425422305323 0 0 0 0 0 0 1.61711697025140 2.77219546898122 1.15508187530801;
0 0 -1.33550608695652 0 0 -5.58823079251630 0 -9.78425422305323 -12.3143655823924 0 0 0 0 0 1.28201098652570 0 1.15508187530801 2.43710327055050;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 -3.30737015738164 1.36517736605472 1.94219279132692 0 0 0 0 0 0 55.5915770671030 -11.6040718529838 -10.5106639714776 0 0 0;
0 0 0 1.36517736605472 -2.55276150142619 0 1.18760382787156 0 0 0 0 0 -11.6040718529838 33.6949232068892 0 -5.97512017854242 0 0;
0 0 0 1.94219279132692 0 -3.22418448881414 0 0 1.28201098652570 0 0 0 -10.5106639714776 0 32.2146426775241 0 0 -5.58823079251630;
0 0 0 0 1.18760382787156 0 -2.80471913975820 1.61711697025140 0 0 0 0 0 -5.97512017854242 0 66.8288576325249 -13.6979757743444 0;
0 0 0 0 0 0 1.61711697025140 -2.77220222213760 1.15508187530801 0 0 0 0 0 0 -13.6979757743444 54.6379749015977 -9.78425422305323;
0 0 0 0 0 1.28201098652570 0 1.15508187530801 -2.43709623841190 0 0 0 0 0 -5.58823079251630 0 -9.78425422305323 79.3225061858399];
rank(A)
ans =
14
Not even close -- only 14 out of 18
A([1 10 11 12], :)
ans = 4×18
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
You have four rows that are all zero. Also columns 10 11 12 are all 0. Any time you have a row or column that is all zero, you are guaranteed that the matrix is singular.

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