Question

For each linear function phi on V, find u is an element of V such that phi(v)= for every v is an element of V:

Answer 1

\[a) \Phi: R ^{3}\rightarrow R, defined by, \Phi(x,y,z)= x+2y-3z\]
\[b) \Phi: C^{3}\rightarrow C, defined by, \Phi(x,y,z)= ix+(2+3i)y+(1-2i)z\]

Answer 2

u can write
\[ \large \Phi(x,y,z)=(x,y,z)\cdot(1,2,-3)=x+2y-3z \]

Answer 3

is this what u mean?