Niech \(\displaystyle{ f: R ^{3} \rightarrow R ^{4}}\),
\(\displaystyle{ f(x _{1},x _{2},x _{3})=(x _{1}+2x _{2}+x _{3},x _{1}+2x _{2}+3x _{3},x _{2}+x _{3}, x _{1}+x _{2}+2x _{3})}\)
Wyznacz bazę \(\displaystyle{ f ^{-1}(V)}\)
gdzie
\(\displaystyle{ V: \begin{cases}x _{1}=x _{2} \\x _{3}=x _{4}\end{cases}}\)