Question

Let $V$ and $W$ be vector spaces and $T: V \to W$ be linear transformation, then

• A. Nullity($T$) is subspace of $W$
• B. Rank($T$) is subspace of $V$
• C. $T(0_V) = 0_W$
• D. $T(0_V) = I$

Hint:

A quick way to check if a transformation is linear is to evaluate it at the zero vector.
If \( T(\mathbf{0}_V) \neq \mathbf{0}_W \), the transformation is not linear (e.g., translation mappings like \( T(x) = x + 3 \)).

Answer 1

The Correct Option is C