I have a matrix of 24 rows x 3 columns. How to obtain all possible combinations of 3 rows? These combinations are then solved for obtaining average value of variables.

LHS is

A=[0.313976809989128  0.177956658855626  78.3488158507844;
35.5174462218438  0.203968398786232  130.746500956281;
2.01021515608203  0.206602303296522  81.6725646419809;
2.24634015155953  0.166640927463375  87.0880600273723;
13.6633712439119  0.199859900476471  94.6371224086545;
15.9528811193948  0.190429321679092  100.278409049176;
37.2448197308362  0.277981859601046  105.603760896428;
37.8682446742245  0.240480046509696  107.589144969063;
44.2889039004173  2.51076959884036  102.000035183270;
47.1249770249307  2.80167184984230  105.283913040282;
49.6287943380623  11.5567315644052  85.1349069485669;
54.8726983927937  12.7472220480560  88.7132665928202;
65.7235732009926  21.0827598977816  91.5677567497500;
62.3808138932447  19.8717817644255  92.7065438895835;
40.4367766528897  15.4158222360858  79.4796533897255;
48.9122996980167  18.3966101694915  85.5014827107762;
59.1385794772328  31.5904929035436  84.9261906960993;
68.4660446264592  36.2437215455307  87.4169710019492;
58.0081090978847  35.5973295200228  90.8130489626749;
58.1667948301691  35.0214232414543  93.8921148117136;
62.5083563651203  39.8111331639183  100.985692468451;
80.9234802795523  52.6140571604828  106.440367866101;
57.4613510889166  35.8566902483007  102.370470245526;
59.0972054988387  37.1450036236640  103.732813275735]

RHS is

C=[37;
39;
45.3;
46.1;
66;
67;
89;
90;
112.5;
115;
134.2;
135;
152.7;
153;
155.1;
156;
175.6;
176;
188.4;
189;
194.2;
194.8;
195;
196]

Considering variables as;

B=[x; y; z]

like

[A]*[B]=[C]

Answer 1

[John D'Errico]

You have 24 rows in A. There are

nchoosek(24,3)
ans =
      2024

sets of possible combinations of rows. You can get the indices of those rows from

C = nchoosek(1:24,3);

Each row of that result represents one desired combination. So, now

A(C(1,:),:)

will give you the first set of three rows as a 3x3 array.

[Stephen23]

+1 nice and clear explanation

Answer 2

[Azzi Abdelmalek]

B=A\C

[Shrikanth]

Thanks for your reply. But, I am sorry to say your answer does not meet my question.

I am looking for possible combination 3 rows from matrix A which will provide matrix A of 3X3. Same is for matrix C. Provided that Rows of matrix A and matrix C have direct relationship. So, its necessary to have same combination for both matrices.

Can you help in this direction?