The KERNEL (null space) of a linear transformation $T : V \to W$ is
Athe image of $T$
Bthe eigenvectors of $T$
Cthe entire space $V$
D$\{v \in V : T(v) = 0\}$
Answer & Solution
Correct answer: D. $\{v \in V : T(v) = 0\}$
1. KERNEL of $T$: $\ker T = \{v \in V : T(v) = 0\}$.
2. The kernel is always a SUBSPACE of $V$.
3. $T$ is INJECTIVE iff $\ker T = \{0\}$.
4. IMAGE of $T$: $\text{im}\,T = \{T(v) : v \in V\}$, a subspace of $W$.
5. Options A, C, D describe other concepts.
_Source: Sergei Treil, "Linear Algebra Done Wrong", §3.2 (Kernel and image)._
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