Base ortonormal para um subespaço de \(R^3\)

Metadata

• CONTEXTO : Primeiro ciclo universitário
• AREA: Matemática
• DISCIPLINA: Álgebra Linear
• ANO: 1
• LINGUA: pt
• AUTOR: Equipa Álgebra Linear
• MATERIA PRINCIPAL: Produtos internos e normas
• DESCRICAO: Ortogo e norm em subespaço
• DIFICULDADE: very easy
• TEMPO MEDIO DE RESOLUCAO: 10 mn
• TEMPO MAXIMO DE RESOLUCAO: 30 mn
• PALAVRAS CHAVE:

Considere o subespaço \(W= \mathscr{L} \)\(\left\{\left(\begin{array}{c}1\\-3\\-3\\\end{array}\right),\left(\begin{array}{c}-3\\3\\1\\\end{array}\right),\left(\begin{array}{c}-8\\12\\8\\\end{array}\right)\right\}\). Diga qual dos seguintes conjuntos é uma base ortonormal para \(W\).

A)\(\left\{\left(\begin{array}{c}\frac{1}{\sqrt{19}}\\-\frac{3}{\sqrt{19}}\\-\frac{3}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}-\frac{21}{\sqrt{646}}\\3\sqrt{\frac{2}{323}}\\-\frac{13}{\sqrt{646}}\\\end{array}\right)\right\}\), B)\(\left\{\left(\begin{array}{c}\frac{1}{\sqrt{19}}\\-\frac{3}{\sqrt{19}}\\-\frac{3}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}-\frac{3}{\sqrt{19}}\\\frac{3}{\sqrt{19}}\\\frac{1}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}-\frac{2}{\sqrt{17}}\\\frac{3}{\sqrt{17}}\\\frac{2}{\sqrt{17}}\\\end{array}\right)\right\}\), C)\(\left\{\left(\begin{array}{c}\frac{1}{19}\\\frac{9}{19}\\\frac{9}{19}\\\end{array}\right),\left(\begin{array}{c}\frac{441}{646}\\\frac{18}{323}\\\frac{169}{646}\\\end{array}\right)\right\}\), D)\(\left\{\left(\begin{array}{c}\frac{1}{\sqrt{19}}\\-\frac{3}{\sqrt{19}}\\-\frac{3}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}-\frac{21}{\sqrt{646}}\\3\sqrt{\frac{2}{323}}\\-\frac{13}{\sqrt{646}}\\\end{array}\right),\left(\begin{array}{c}-\frac{2}{\sqrt{17}}\\\frac{3}{\sqrt{17}}\\\frac{2}{\sqrt{17}}\\\end{array}\right)\right\}\)

Para obter o zip que contém as instâncias deste exercício clique aqui[1]

Se deseja obter o código fonte que gera os exercícios contacte miguel.dziergwa@ist.utl.pt