MathAlgebraLinear algebraLinear operators

Null space and range

Transforming a small space into a larger one

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Intuitively, the surjective transformations $T: \, V \rightarrow W$ fill all the $W$ space.

But what happens if $W$ is greater than $V$ , that is, the dimension of $W$ is greater than that of $V$ .

Can $T$ be surjective?

Hint: When $T$ is surjective, $\operatorname{Im} \, T = W$ .

Select one option from the list

Some transformations are surjective but not all

No transformation can be surjective

Any transformation is surjective

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