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Related

rank

rank([[2,0,1,1,1,2,0,...

Calculate

rank

V1:[1,0,2];

V2:[-2,1,1];

V3:[0,1,5];

Calculate

rank

eq1: a1 - 2*a2 + a3 = 0;

eq2: a4 - 2*a5 + a6 = 0;

eq3: a7 - 2*a8 + a9 = 0;

Calculate

rank

rank([[1,1,0,0,1,1,0]...

Calculate

rank

rank([[1,1],[1,0]]);

Calculate

rank

rank([[1,2],[3,4]]);

Calculate

rank

rank([[2,0,1,1,1,2,0,...

Calculate

rank

eq1: a1 - 2*a2 + a3 = 0;

eq2: a4 - 2*a5 + a6 = 0;

eq3: a7 - 2*a8 + a9 = 0;

Calculate

rank

Run Example
(%i1)for i:1 thru 200 step 1 do block(a11: rand_with_step(-2,2,1), a12: rand_with_prohib(-2,2,[0]), a13: rand_with_prohib(-2,2,[ sqrt(1-a11^2-a12^2) ]), a21: rand_with_step(-2,2,1),a22: rand_with_step(-2,2,1), a23: rand_with_prohib(-2,2,[sqrt(1-a21^2-a22^2)]), a31: rand_with_step(-2,2,1), a32: rand_with_step(-2,2,1), a33: rand_with_prohib(-2,2,[ sqrt(1-a31^2-a32^2) ] ), a1: [a11,a12,a13], a2: [a21,a22,a23], a3: [a31,a32,a33], M: matrix([a1,a2,a3]), R: rank(M), if R = 3 then return(M) );
(%o1)                                done
(%i2) R;
(%o2)                                  1
(%i3) 
Run Example
a: matrix ([9,2,10], [-3,4,0], [1,3,0], [4,0,-7], [0,1,0]);
                                [  9   2  10  ]
                                [             ]
                                [ - 3  4   0  ]
                                [             ]
(%o1)                           [  1   3   0  ]
                                [             ]
                                [  4   0  - 7 ]
                                [             ]
                                [  0   1   0  ]
(%i2) nullity(a);
(%o2)                                  0
(%i3) rank(a);
(%o3)                                  3
(%i4) 
Run Example
v1:[1,0,1];
(%o1)                              [1, 0, 1]
(%i2) v2:[0,1,0];
(%o2)                              [0, 1, 0]
(%i3) v3:[0,1,1];
(%o3)                              [0, 1, 1]
(%i4) v4:[1,2,3];
(%o4)                              [1, 2, 3]
(%i5) v5:[1,3,0];
(%o5)                              [1, 3, 0]
(%i6) v6:[3,2,3];
(%o6)                              [3, 2, 3]
(%i7) B1:matrix(v1,v2,v3);
                                  [ 1  0  1 ]
                                  [         ]
(%o7)                             [ 0  1  0 ]
                                  [         ]
                                  [ 0  1  1 ]
(%i8) B2:matrix(v4,v5,v6);
                                  [ 1  2  3 ]
                                  [         ]
(%o8)                             [ 1  3  0 ]
                                  [         ]
                                  [ 3  2  3 ]
(%i9) rank(B1);
(%o9)                                  3
(%i10) rank(B2);
(%o10)                                 3
(%i11) A:B2.(invert(B1));
                                 [ 1  0   2  ]
                                 [           ]
(%o11)                           [ 1  4  - 1 ]
                                 [           ]
                                 [ 3  2   0  ]
(%i12) 
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