Matrix is singular to working precision

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Vladik Berg
Vladik Berg on 28 Apr 2022
Answered: Walter Roberson on 28 Apr 2022
M = [0 0 0 0 -1 0 0 0 0 0 1 0 ;
0 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 -R -1 ;
1 0 0 0 0 0 0 0 -1 0 -1 0;
0 -1 0 0 0 0 0 1 0 0 0 0;
(-OA/2) 0 0 0 0 0 0 0 (-OA/2) 0 R 0;
-1 0 1 0 0 0 0 0 0 0 0 0;
0 1 0 1 0 0 0 0 0 0 0 0;
(-0.4*sind(20)) (-0.4*cosd(20)) (-0.4*sind(20)) (0.4*cosd(20)) 0 0 0 0 0 0 0 0;
0 0 1 0 0 0 -1 0 0 0 0 0;
0 0 0 -1 0 0 0 1 0 0 0 0;
0 0 (BD/2) 0 0 0 (BD/2) 0 0 0 0 0];
X = [(0);
(mDrum*G);
(mDrum*RDrum^2.*alpha);
(mOA*acOAx);
(mOA*G*acOAy);
((1/12)*(OA)*(0.3)^2.*aaOA);
(mOA*acABx);
(mOA*G*acABy);
((1/12)*(mAB)*(AB)^2.*aaAB);
(mBD*acBDx);
(mBD*G*acBDy);
((1/12)*(mBD)*(BD)^2.*aaBD)];
Forces = M\X
can anyone see whats wrong? i only get NaN exept the last entry there i get inf
  1 Comment
KSSV
KSSV on 28 Apr 2022
All the varibles are not defined.

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Answers (2)

Walter Roberson
Walter Roberson on 28 Apr 2022
Look at the third-last column of M, and notice that it is all zero. When you have a column that is all zero then the column rank of the matrix is reduced by 1. By symmetry in the way determinants are calculated, for square matrices that implies the row rank is also reduced by 1. So your rank is at most 11.
syms R OA BD
Sind = @(x) sind(sym(x));
Cosd = @(x) cosd(sym(x));
M = [0 0 0 0 -1 0 0 0 0 0 1 0 ;
0 0 0 0 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 -R -1 ;
1 0 0 0 0 0 0 0 -1 0 -1 0;
0 -1 0 0 0 0 0 1 0 0 0 0;
(-OA/2) 0 0 0 0 0 0 0 (-OA/2) 0 R 0;
-1 0 1 0 0 0 0 0 0 0 0 0;
0 1 0 1 0 0 0 0 0 0 0 0;
(-0.4*Sind(20)) (-0.4*Cosd(20)) (-0.4*Sind(20)) (0.4*Cosd(20)) 0 0 0 0 0 0 0 0;
0 0 1 0 0 0 -1 0 0 0 0 0;
0 0 0 -1 0 0 0 1 0 0 0 0;
0 0 (BD/2) 0 0 0 (BD/2) 0 0 0 0 0];
M
M = 
size(M)
ans = 1×2
12 12
rank(M)
ans = 11

Jan
Jan on 28 Apr 2022
Why do you assume, that something is wrong? The provided matrix is near to singular. In 1-D this would mean, that you try to divide by a number, which is almost zero. This is not a bug, but a mathematical observation.
Maybe there is a typo in the definition of M. There is no chance that the readers can guess, where it is.
The accessive use of parentheses in the definition of X is an overkill. It impedes the reading only. For writing M it is safer to separate the columns with commas to avoid ambiguities.

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