Problem with x=A\B. Bottom rows of answer equals to zero.

I am solving A = [0.063950442420678 -0.079659325686456 0.703185937004828 -0.703629356084602 0.196116135138184 0;

-0.063972494502836  -0.079635254048311  -0.705228608870820  -0.701582750279591                   0   0.196116135138184;

   0.704092141618340  -0.702722541685005  -0.063847146141638   0.079742256355280   0.980580675690920                   0;

-0.704323872215463  -0.702491030228577   0.064075651837015   0.079552160985497                   0   0.980580675690920;]

B = 1.0e+16 *[

-0.008393560875461   0.007176612465150  -0.002567658626434   0.001955625630576;
 0.008396455233765   0.007174443819898   0.002575117370646   0.001949937415988;
-2.310320315585672   1.582729739656721   0.005828390008126  -0.005540772248194;
 2.311080687523706   1.582208310436191  -0.005849249520136  -0.005527563753758]

X=A\B;

But the answer I got is

X = [ 1.0e+16 *

-3.255501591781910   0.000000468614428   0.007894550087601  -0.000007698327826
 0.000000682708769  -2.224850034252500   0.000012772109782   0.007465621932653
 0.283767705911329   0.000315121768850  -0.004368508422496  -0.000000402964920
-0.000363544285286   0.241995389630699  -0.000000529410532  -0.003625641380985
                 0                   0                   0                   0
                 0                   0                   0                   0]

Bottom rows are all zeros.

I tried Pinv, QR method too. But the results are not accurate. Any suggestions??

Answer 1

[Roger Stafford]

The equations you are trying to solve with X = A\B are given by:

   A*X = B

where from the sizes of A and B, X must be of size 6 x 4. For each column of X you have four equations and six unknowns, making a total of sixteen equations and twenty-four unknowns, so this problem is highly indeterminate. There are infinitely many possible solutions. In other words the values in A and B are insufficient to deduce completely what values X must have had. Consequently matlab arbitrarily set eight of the X values to zero. It is no surprise that these don't match your original values in X. To reconstruct X you need enough additional information to pin down eight more degrees of freedom.

[Babu]

Thank you Roger. I took additional values and it worked.