Question

Let $T : U(F) \to V(F)$ be a linear transformation, then which of the following holds:
A. $\text{Rank}(T) + \text{dim}(V) = \text{Nullity}(T)$ B. $\text{Rank}(T) + \text{Nullity}(T) = \text{dim}(U)$ C. $\text{Nullity}(T) = \text{dim}(V)$ D. $\text{Nullity}(T) = \text{dim}(\text{Ker}(T))$ E. $\text{Nullity}(T) = \text{dim}(U)$ Choose the correct answer from the options given below:

• A. B, C, E Only
• B. B, D Only
• C. A, D Only
• D. A, C Only

Hint:

Always remember: $\text{Rank}(T) + \text{Nullity}(T) = \text{dim}(\text{Domain})$. The codomain dimension $\text{dim}(V)$ does not appear in the theorem!

Answer 1

The Correct Option is B