Hi,(adsbygoogle = window.adsbygoogle || []).push({});

My question is to show that the linear transformation T: M_{2x2}(F) -> P_{2}(F) defined by

T (a b c d) = (a-d) | (b-d)x | (c-d)x^{2}

is surjective but not injective.

thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Show that linear transformation is surjective but not injective

**Physics Forums | Science Articles, Homework Help, Discussion**