Question

Linear transformation
Is this linear trandformation?
L([x,y,z]) = [0,0,0]

Thank you!

Answer 1

Question #15350 Is this linear transformation? $L([x,y,z]) = [0,0,0]$

Solution.. One need to verify, whether $L(\alpha_{1}[x_{1},y_{1},z_{1}] + \alpha_{2}[x_{2},y_{2},z_{2}]) = \alpha_{1}L([x_{1},y_{1},z_{1}]) + \alpha_{2}L([x_{2},y_{2},z_{2}])$ for any $\alpha_{1},\alpha_{2}$ and $[x_i,y_i,z_i],i = 1,2$ . But this obviously holds, due to both sides equal zero.