MathAlgebraLinear algebraLinear operators

Introduction to linear operators

Operator action

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Suppose we have a linear operator B\mathcal{B}, which matrix is (3124)\begin{pmatrix} 3 & -1 \\ 2 & 4 \end{pmatrix}, and a vector v=(3,0)v = (3, 0). What Bv\mathcal{B}v is equal to?

1) It is not a linear operator.

2) (96)\begin{pmatrix} 9 \\ 6 \end{pmatrix};

3) (82)\begin{pmatrix} 8 \\ 2 \end{pmatrix};

4) (9060)\begin{pmatrix} 9 & 0 \\ 6 & 0 \end{pmatrix}.

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