matrix transformations for L(x,y,z)= (2x+4y-2z, x+y+4z)

[mathstresser]

Let L: R^3 -> R^2 be defined by L(x,y,z)= (2x+4y-2z, x+y+4z). Find the standard matrix representing L.

I know that

. . .\(\displaystyle \L A\, =\, \left[\, \begin{array}{rr}2&4&-2\\1&1&4\\0&0&0\end{array}\, \right]\)

is not right.

But why not? What else should I do?

 

[tkhunny]

Overthinking? Will a 3x3 matrix get you to R2? Why not delete the third row and think it over again?