# Gauss Elimination Method with partial pivoting

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.

• 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? – KittyL Feb 24 '15 at 9:56
• both sides are not equal for pivoting solution but equal for solution without pivoting. – Pan Kuji Feb 24 '15 at 13:14

$$0.7879\\ 11.9493\\ 16.3319$$
$$0.7919\\ 11.9933\\ 24.2839$$