MathAlgebraLinear algebraLinear operators

Actions with linear operators

Operator square

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You have the following square matrix:

A = \begin{pmatrix} 1 &0& 1 \\ 0&1&2 \\1 &-1 & 1 \end{pmatrix}

What is the value of $(L_A) ^2$ in any vector $x$ ?

Select one option from the list

(L_A)^2 \, (x) = \begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 2 \\ 1 & -1 & 0 \end{pmatrix}x

(L_A)^2 \, (x) = \begin{pmatrix} 2 & -1 & 2 \\ 2 & -1 & 4 \\ 2 & -2 & 0 \end{pmatrix}x

(L_A)^2 \, (x) = \begin{pmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 1 & -1 & 1 \end{pmatrix}x

(L_A)^2

is not a linear operator.

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