Chapter 6.2, Problem 66E

To determine

(a)

Whether the statement “The dimension of a linear transformation $T$ from a vector space $V$ into a vector space $W$ is the rank of $T$.” is true or false.

To determine

(b)

Whether the statement “A linear transformation $T$ from $V$ into $W$ is one-to-one when the preimage of every $w$ in the range consists of a single vector $v$.” is true or false.

To determine

(c)

Whether the statement “The vector spaces $R^2$ and $P_1$ are isomorphic to each other.” is true.