MathAlgebraLinear algebraLinear operators

Linear operators and matrices

A linear operator and zero vector

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Is the following statement true or false?

"Any linear operator $\mathcal{A}$ takes a zero vector to a zero vector: $\mathcal{A}0 = 0.$ "

Select one option from the list

It depends on a vector space.

This statement is false.

This statement is true.

It depends on a linear operator.

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