MHB How Do Basis and Vectors Work in Linear Algebra?

[Kaspelek]

Hi guys,

I'm back and have another Linear Albgera question!

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Thanks in advance.

No idea how to start

 

[Fernando Revilla]

In both cases, you only need to apply the definition of coordinates. For $(a)$ express $v=x_1(1,0,1)+x_2(1,1,0)+x_3(0,1,1)$, solve the system and $[v]_{\mathcal{B}}=(x_1,x_2,x_3)^T$. For $(b)$, $w=1v_1+2v_2-3v_3$, where $\mathcal{B}=\{v_1,v_2,v_3\}$. Let us see what do you obtain.