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We got following system of equation :

$0.61X+1.23Y+1.72Z=0.792$

$1.02X+2.15Y-5.51Z=12.0$

$-4.34X+11.2Y-4.25Z=16.3$

with partial pivoting solution set is $\left \{1.59,1.6,-1.25 \right \}$. If the same problem is solved without pivoting the solution set is $\left \{0.79,2.00,-1.25 \right \}$.

When we plugin $\left \{1.59,1.6,-1.25 \right \}$ in first equation we get $0.7363$ on LHS which is not equal to $0.792$ But when we plugin $\left \{0.79,2.00,-1.25 \right \}$ in first equation we get $0.7919$ or $ 0.792$ on LHS which is equal to $0.792 $ on RHS.

Why is the solution set $\left \{0.79,2.00,-1.25 \right \}$ without pivoting unacceptable ? In my book the reason is that 0.79 is not even correct to one significant figure.

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    $\begingroup$ You said when you plug in the pivoting solution {1.59,1.6,-1.28} you didn't get the right answer, but when you plug in the one with pivoting you got the right answer. Did you state the wrong way? $\endgroup$ – KittyL Feb 24 '15 at 9:56
  • $\begingroup$ both sides are not equal for pivoting solution but equal for solution without pivoting. $\endgroup$ – Pan Kuji Feb 24 '15 at 13:14
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If you plug in the pivoting solution, you get

$$ 0.7879\\ 11.9493\\ 16.3319$$

which is close enough to the right hand side.

If you plug in the non-pivoting solution, you get

$$ 0.7919\\ 11.9933\\ 24.2839$$

You can see the 3rd one is very far from the original.

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