- #1

- 719

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Is the subset A a subspace of W

[tex]W=\left \{ \begin{bmatrix}

1 &1 \\

a_{21}& a_{22} \\

a_{31}& a_{32}

\end{bmatrix} :a_{ij} \in \mathbb{C}\right \}[/tex]

Let [tex]A=\begin{bmatrix}

1 &1 \\

a_{21}& a_{22}\\

a_{31}& a_{32}

\end{bmatrix}[/tex]

[tex]A \in W[/tex]

Then [tex]2A \in W[/tex] since

[tex]2A=2\begin{bmatrix}

1 &1 \\

a_{21}& a_{22}\\

a_{31}& a_{32}

\end{bmatrix}[/tex]

Is this correct? My notes is telling its NOT closed under scalar multiplication which I dont think is correct.

[tex]W=\left \{ \begin{bmatrix}

1 &1 \\

a_{21}& a_{22} \\

a_{31}& a_{32}

\end{bmatrix} :a_{ij} \in \mathbb{C}\right \}[/tex]

Let [tex]A=\begin{bmatrix}

1 &1 \\

a_{21}& a_{22}\\

a_{31}& a_{32}

\end{bmatrix}[/tex]

[tex]A \in W[/tex]

Then [tex]2A \in W[/tex] since

[tex]2A=2\begin{bmatrix}

1 &1 \\

a_{21}& a_{22}\\

a_{31}& a_{32}

\end{bmatrix}[/tex]

Is this correct? My notes is telling its NOT closed under scalar multiplication which I dont think is correct.

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