Olá, Ale21.
[tex]u = (3, -1)\text{ e }v =(-1,2)\\\\\\ a)\ 4 (u - v) + \frac13 w = 2u - w \Rightarrow \\\\ 4[(3,-1)-(-1,2)]+\frac13(w_1,w_2)=2(3, -1)-(w_1,w_2)\Rightarrow\\\\ 4[(4,-3)]+\frac13(w_1,w_2)=(6,-2)-(w_1,w_2) \Rightarrow\\\\ \frac13(w_1,w_2)+(w_1,w_2)=(6,-2)-(16,-12) \Rightarrow\\\\ \frac43(w_1,w_2)=(-10,10) \Rightarrow (w_1,w_2)=\frac34(-10,10) \Rightarrow\\\\ \boxed{w=(w_1,w_2)=(-\frac{15}2,\frac{15}2)}[/tex]
[tex]b)\ 3w - (2v - u) = 2 ( 4w - 3 u) \Rightarrow \\\\ 3(w_1,w_2)-[2(-1,2)-(3,-1)]=2[4(w_1,w_2)-3(3,-1)] \Rightarrow \\\\ 3(w_1,w_2)-[(-2,4)-(3,-1)]=8(w_1,w_2)-6(3,-1) \Rightarrow \\\\ -5(w_1,w_2)=(-18,6)+(-5,5) \Rightarrow \\\\ (w_1,w_2)=\frac15(-23,11) \Rightarrow \\\\ \boxed{w=(w_1,w_2)=(-\frac{23}5,\frac{11}5)}[/tex]
