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

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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??

采纳的回答

Roger Stafford
Roger Stafford 2014-6-5
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.

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