Are the following true or false? If it is true, prove it, if it is false give a counter example (and proof that your counter example is true).

1) IfTis a linear transformation such thatT: $\displaystyle R^2$ -> $\displaystyle R^3$,Tcan't be one to one.

2) If a matrix has characteristic polynomial $\displaystyle f(x) = (x-2)^2(x+4)(x-4)$, then the matrx is not diagonalizable.