Esercizio 3.41 Consideriamo i sottospazi begin {aligned}& V= operatorname {Span}((1,-1,2,0)^{ top },(1,1,1,0)^{ top },(1,3,0,0)^{T},(-1,-1,0,0)^{T}) & W= left {( begin {array}{l}x_1 x _2 x _3 x _4 end {array}): x_1-x_2=0,-x_1+2 x_2=0 right } end {aligned} i) Calcolare V+W, operatorname {dim}(V+W)$.ii.) Calcolare operatorname {dim} V, operatorname {dim} W, operatorname {dim} V oplus W. [attach]93027[/attach] Esercizio geometria 1

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Esercizio 3.41 Consideriamo i sottospazi

$$
\begin{aligned}
& V=\operatorname{Span}\left((1,-1,2,0)^{\top},(1,1,1,0)^{\top},(1,3,0,0)^{\mathrm{T}},(-1,-1,0,0)^{\mathrm{T}}\right) \\
& W=\left\{\left(\begin{array}{l}
x_1 \\
x_2 \\
x_3 \\
x_4
\end{array}\right): x_1-x_2=0,-x_1+2 x_2=0\right\}
\end{aligned}
$$

i) Calcolare $V+W$, $\operatorname{dim}(V+W)$.
ii.) Calcolare $\operatorname{dim} V, \operatorname{dim} W, \operatorname{dim} V \oplus W$.