Question

Lin Alg question...

L: R^3 --> R^2 defined by L((x,y,z)) =xz

..is it LINEAR or NOT LINEAR..explain the steps i'm pretty stuck on it!
Thx.
D55.

Answer 1

really all i know is L(x +y +z)= Lx + Ly + Lz and L(cx) = cL(u) if its linear... dont really know what to do with that tho

Answer 2

L(cx)=cL(x)**

Answer 3

\(L((x_1,y_1,z_1)+(x_2,y_2,z_2))=L((x_1+x_2,y_1+y_2,z_1+z_2))=(x_1+x_2)(z_1+z_2)\).
\(L(x_1,y_1,z+1)+L(x_2,y_2,z_2)=x_1z_1+x_2z_2\ne(x_1+x_2)(z_1+z_2)\) . So it's NOT lineaer.

Answer 4

There is a typo in the second line. It should be \(z_1\) not z+1.

Answer 5

thanks anwar
appreciate it once again!

Answer 6

You're welcome :)

Answer 7

donny r u here?