Question

Resolver o exercício de álgebra linear, preciso resolver até amanhã alguém me ajuda?????

Answer 1

Explicação passo-a-passo:

a)

$Verificar \: que\: vale: \\ \blue{ 1) }\: 0 \in \: W \\ \blue{2) }\: u + v \in \: W \\ \blue{3) }\: \alpha u \in \: W \\ \\ v = (x,0) \\ \\ \blue{1)}\:Para \: x = 0 \: temos : \\ (x,0) = (0,0) \in \: W \\ \\ \blue{2)}\:u = (x1,0) \\ v = (x2,0) \\ \\ u + v = \\ \\ = (x1,0) + (x2,0) \\ \\ = (x1 + x2,0 + 0) \\ \\ = (x1 + x2,0) \in \: W \\ \\ \blue{3) }\;\alpha u = \\ \\ = \alpha ( + x1,0) \\ \\ = ( \alpha x1, \alpha \sdot0) \\ \\ = ( \alpha x1,0) \in \: W \\ \\ \Large \boxed{\green{\bf Sim \: é \: subespaço\:de\:V}}$

b)

$\Large\left({{x \: - x} \atop{z \: \: \: \: \: \: t}} \right) \\ \\\blue{ 1)} \: \: para \: x = 0 \\ z = 0 \\ t = 0 \\ \\ \large\left({{0 \: - 0} \atop{0 \: \: \: \: \: \: 0}} \right) = \\ \\ = \large\left({{0\: \: \: \: \: \: 0} \atop{0\: \: \: \: \: \: 0}} \right) \in \: W \\ \\ \blue{2)} \: A = \large\left({{x\: \: \: - x} \atop{z\: \: \: \: \: \: \: \: t}} \right) \\ \\ B = \Large\left({{x\: \: \: - x} \atop{a\: \: \: \: \: \: \: \: b}} \right) \\ \\ A + B = \\ \\ = \Large\left({{x\: \: \: - x} \atop{z\: \: \: \: \: \: \: \: t}} \right) + \Large\left({{x\: \: \: - x} \atop{a\: \: \: \: \: \: \: \: b}} \right) \\ \\ = \Large\left({{x + x\: \: \: - x- x} \atop{z + a\: \: \: \: \: \: \: \: t + b}} \right) \\ \\ = \Large\left({{2x\: \: \: - 2x} \atop{z + a\: \: \: \: \: \: \: \: t + b}} \right) \in \: W \\ \\ \blue{3)} \: \alpha .A = \\ \\ = \alpha .\Large\left({{x\: \: \: - x} \atop{z\: \: \: \: \: \: \: \: t}} \right) \\ \\ = \Large\left({{ \alpha x\: \: \: - \alpha x} \atop{ \alpha z\: \: \: \: \: \: \: \: \alpha t}} \right) \in \: W \\ \\ \Large \boxed{\green{\bf Sim \: é \: subespaço\:de\:V}}$

$\Large \boxed{\underline{\bf \blue{Bons \:Estudos!}}}\\ \\ \Large \boxed{\underline{\bf27/05/2021}}$