MathAlgebraLinear algebraLinear operators

Actions with linear operators

The product of operators

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You need to lead with the following matrices: $A = \begin{pmatrix} 1 & 2 \\ 3 & -1 \end{pmatrix} \quad B= \begin{pmatrix} -1 &0 \\ 2 & 1 \end{pmatrix}$ What is the value of $L_B \circ L _A$ in any vector $x$ ?

Select one option from the list

\begin{pmatrix} -1 & -2 \\ 5 & 3 \end{pmatrix}x

L_A

and

L_B

are not linear operators

\begin{pmatrix} 1 & 2 \\ 3 & -1 \end{pmatrix} x

\begin{pmatrix}3 & 2 \\ -5 & -1\end{pmatrix} x

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