Balancing chemical reactions, issues of Gauss's elimination method
Your "should-be" solution,

$$\ce{3H2O2 + 2NO3- + 2H+ → 3O2 + 2NO + 4H2O}$$

is a linear combination of

$$\ce{H2O2 + 2NO3- + 2H+ → 2O2 + 2NO + 2H2O}$$

and 

$$\ce{2H2O2  → O2 +  2H2O}$$

Any other linear combination is valid as well.