Exercise · ZW-RANK-NULLITY-THEOREM-003 · ★☆☆ Basic
A linear map defined on a space of dimension \(6\) has a kernel of dimension \(2\). What is the dimension of its image?
Choose one option.
Show answer
- D. \(4\)
Explanation
\(\dim\operatorname{Im}T=6-2=4\).
Review the concept: Rank–nullity theorem
For a linear transformation \(T\) with finite-dimensional domain \(V\), the dimension of the kernel plus that of the image equals the dimension of \(V\).
\[\dim V=\dim\ker T+\dim\operatorname{Im}T\]
More practice problems: rank–nullity theorem
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