MathAlgebraLinear algebraLinear operators

Introduction to linear operators

What about this mapping

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Suppose we have a mapping $\mathcal{B} \colon \mathbb{R}^2 \to \mathbb{R}^2$ , which is defined by the following rule: for any vector $v = (v_1, v_2) \in \mathbb{R}^2$

$\mathcal{B}v = \begin{pmatrix} v_1+v_2^2 \\ v_1 - v_2 \end{pmatrix}.$ Is $\mathcal{B}$ a linear operator?

Select one option from the list

Yes, it is a linear operator.

It is not a mapping.

It is an operator, but it is not linear.

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