RREF not giving reduced echelon form

Question

Adnan Jahangir 2015-10-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/247801-rref-not-giving-reduced-echelon-form

编辑： Walter Roberson 2015-10-10

Dear!

I am having a system of 5 linear equations, with 5 unknowns to be determined. When I use the command of rref (A) on the matrix A (Augmented matrix) then instead of reduced echelon form it gives all the entries in first row, and making remaining 4 rows as zero rows, could not understand why is happening so.

1) here I represent the part of program where I represented this operation

for i=2:1:length(O)
QQQ =[M1(i,1) M1(i,2) M1(i,3) M14(i,1) 0 b1(i,1);M2(i,1) M2(i,2) M2(i,3) M24(i,1) 0 b2(i,1);M3(i,1) M3(i,2) M3(i,3) 0 0 b3(i,1);M4(i,1) M4(i,2) M4(i,3) 0 M45(i,1) b4(i,1);M5(i,1) M5(i,2) M5(i,3) 0 M55(i,1) b5(i,1)];
RR=rref(QQQ)
II(i,:) =RR(1,6)
end

where each M is defined properly,

result for the value of i=2 are as follows

-3.6035e+050 -1.0331e+035i  3.2541e+021 +6.1677e+019i  -5.1763e+020 -2.5318e+020i  -2.3565e+019  0  7.2761e+018
0.12558 -8.6149e+014i  -2.5881 -   0.024521i  0.24839 -     1.0585i  -0.99606  0  0.86678
-2.1361e+049 +4.8846e+064i  -1.2606e+021 -3.7042e+019i  -6.8697e+019 +1.0156e+020i  0  0  7.1063e+048 +2.0718e+033i
-1.513e+017 + 1.038e+033i  -2.1573e+005 -       6339i  -7837.5 +      11586i  0  0.0050625 -  7.79e+013i  -1.5087e+017 -9.9402e-015i
2.1361e+059 -4.8846e+074i  1.2606e+031 +3.7042e+029i  6.8697e+029 -1.0156e+030i  0  0.00021977 -3.0093e-036i  -7.1063e+058 -2.0718e+043i

in command window it looks alike

1.0e+074 *
    Columns 1 through 5 
    -0.0000 - 0.0000i   0.0000 + 0.0000i  -0.0000 - 0.0000i  -0.0000                  0          
     0.0000 - 0.0000i  -0.0000 - 0.0000i   0.0000 - 0.0000i  -0.0000                  0          
    -0.0000 + 0.0000i  -0.0000 - 0.0000i  -0.0000 + 0.0000i        0                  0          
    -0.0000 + 0.0000i  -0.0000 - 0.0000i  -0.0000 + 0.0000i        0             0.0000 - 0.0000i
     0.0000 - 4.8846i   0.0000 + 0.0000i   0.0000 - 0.0000i        0             0.0000 - 0.0000i
    Column 6 
     0.0000          
     0.0000          
     0.0000 + 0.0000i
    -0.0000 - 0.0000i
    -0.0000 - 0.0000i

after applying rref(QQQ) I get

-7.5834e-046 +2.5808e-044i  2.0791e-045 +1.4064e-045i  0  1.9676e-094 +4.4992e-079i  -2.1208e-032 -1.4548e-016i
0  0  0  0  0
0  0  0  0  0
0  0  0  0  0
0  0  0  0  0

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Walter Roberson 2015-10-10

编辑：Walter Roberson 2015-10-10

To help people with data entry for testing:

M = [-3.6035e+50-1.0331e+35i 3.2541e+21+6.1677e+19i -5.1763e+20-2.5318e+20i -2.3565e+19 0 7.2761e+18;0.12558-861490000000000i -2.5881-0.024521i 0.24839-1.0585i -0.99606 0 0.86678;-2.1361e+49+4.8846e+64i -1.2606e+21-3.7042e+19i -6.8697e+19+1.0156e+20i 0 0 7.1063e+48+2.0718e+33i;-1.513e+17+1.038e+33i -215730-6339i -7837.5+11586i 0 0.0050625-77900000000000i -1.5087e+17-9.9402e-15i;2.1361e+59-4.8846e+74i 1.2606e+31+3.7042e+29i 6.8697e+29-1.0156e+30i 0 0.00021977-3.0093e-36i -7.1063e+58-2.0718e+43i]

In in Maple,

M := Matrix(5,6, [[-0.36035e51-0.10331e36*I, 0.32541e22+0.61677e20*I, -0.51763e21-0.25318e21*I, -0.23565e20, 0, 0.72761e19], [.12558-0.8614900000e15*I, -2.5881-0.24521e-1*I, .24839-1.0585*I, -.99606, 0, .86678], [-0.21361e50+0.48846e65*I, -0.12606e22-0.37042e20*I, -0.68697e20+0.10156e21*I, 0, 0, 0.71063e49+0.20718e34*I], [-0.1513e18+0.1038e34*I, -215730-6339*I, -7837.5+11586.*I, 0, 0.50625e-2-0.7790000000e14*I, -0.15087e18-0.99402e-14*I], [0.21361e60-0.48846e75*I, 0.12606e32+0.37042e30*I, 0.68697e30-0.10156e31*I, 0, 0.21977e-3-0.30093e-35*I, -0.71063e59-0.20718e44*I]])

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