MathAlgebraLinear algebraLinear operators

Null space and range

A constant transformation

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Consider the constant transformation $\mathscr{O}: V\rightarrow W$ given by $\mathscr{O}(v)=0$ for all $v \in V$ .

What does its null space look like?

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\ker(\mathscr{O}) = W

\ker(\mathscr{O}) = \{ 0 \}

\ker(\mathscr{O}) = V \cap W

\ker(\mathscr{O}) = V

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