Diferenças entre edições de "Ortogonalização e normalização"
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| − | Considere a seguinte base de \( \mathbb{R³}\) \(\left\{\left(\begin{array}{c}3\\ | + | Considere a seguinte base de \( \mathbb{R³} \) \(\left\{\left(\begin{array}{c}-3\\3\\-1\\\end{array}\right),\left(\begin{array}{c}-2\\-3\\0\\\end{array}\right),\left(\begin{array}{c}2\\2\\2\\\end{array}\right)\right\}\). Diga qual dos seguintes conjuntos corresponde á ortonormalização desta base. |
| − | A)\(\left\{\left(\begin{array}{c}\frac{3}{\sqrt{ | + | A)\(\left\{\left(\begin{array}{c}-\frac{3}{\sqrt{19}}\\\frac{3}{\sqrt{19}}\\-\frac{1}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}-\frac{47}{\sqrt{4522}}\\-24\sqrt{\frac{2}{2261}}\\-\frac{3}{\sqrt{4522}}\\\end{array}\right),\left(\begin{array}{c}-\frac{3}{\sqrt{238}}\\\sqrt{\frac{2}{119}}\\\frac{15}{\sqrt{238}}\\\end{array}\right)\right\}\), |
| − | B)\(\left(\begin{array}{ | + | B)\(\left\{\left(\begin{array}{c}-\frac{2}{\sqrt{13}}\\-\frac{3}{\sqrt{13}}\\0\\\end{array}\right),\left(\begin{array}{c}-\frac{45}{\sqrt{3094}}\\15\sqrt{\frac{2}{1547}}\\-\sqrt{\frac{13}{238}}\\\end{array}\right),\left(\begin{array}{c}-\frac{3}{\sqrt{238}}\\\sqrt{\frac{2}{119}}\\\frac{15}{\sqrt{238}}\\\end{array}\right)\right\}\), |
| − | C)\(\left(\begin{array}{ | + | C)\(\left\{\left(\begin{array}{c}\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\end{array}\right),\left(\begin{array}{c}-2\sqrt{\frac{2}{21}}\\\frac{5}{\sqrt{42}}\\-\frac{1}{\sqrt{42}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{2}{7}}\\-\frac{1}{\sqrt{14}}\\\frac{3}{\sqrt{14}}\\\end{array}\right)\right\}\), |
| − | D)\(\left(\begin{array}{ | + | D)\(\left\{\left(\begin{array}{c}-\frac{3}{\sqrt{19}}\\\frac{3}{\sqrt{19}}\\-\frac{1}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}4\sqrt{\frac{2}{133}}\\\frac{11}{\sqrt{266}}\\\frac{9}{\sqrt{266}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{2}{7}}\\-\frac{1}{\sqrt{14}}\\\frac{3}{\sqrt{14}}\\\end{array}\right)\right\}\) |
Revisão das 09h23min de 28 de julho de 2016
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: easy
- TEMPO MEDIO DE RESOLUCAO: 10 mn
- TEMPO MAXIMO DE RESOLUCAO: 30 mn
- PALAVRAS CHAVE:
Considere a seguinte base de \( \mathbb{R³} \) \(\left\{\left(\begin{array}{c}-3\\3\\-1\\\end{array}\right),\left(\begin{array}{c}-2\\-3\\0\\\end{array}\right),\left(\begin{array}{c}2\\2\\2\\\end{array}\right)\right\}\). Diga qual dos seguintes conjuntos corresponde á ortonormalização desta base.
A)\(\left\{\left(\begin{array}{c}-\frac{3}{\sqrt{19}}\\\frac{3}{\sqrt{19}}\\-\frac{1}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}-\frac{47}{\sqrt{4522}}\\-24\sqrt{\frac{2}{2261}}\\-\frac{3}{\sqrt{4522}}\\\end{array}\right),\left(\begin{array}{c}-\frac{3}{\sqrt{238}}\\\sqrt{\frac{2}{119}}\\\frac{15}{\sqrt{238}}\\\end{array}\right)\right\}\), B)\(\left\{\left(\begin{array}{c}-\frac{2}{\sqrt{13}}\\-\frac{3}{\sqrt{13}}\\0\\\end{array}\right),\left(\begin{array}{c}-\frac{45}{\sqrt{3094}}\\15\sqrt{\frac{2}{1547}}\\-\sqrt{\frac{13}{238}}\\\end{array}\right),\left(\begin{array}{c}-\frac{3}{\sqrt{238}}\\\sqrt{\frac{2}{119}}\\\frac{15}{\sqrt{238}}\\\end{array}\right)\right\}\), C)\(\left\{\left(\begin{array}{c}\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\end{array}\right),\left(\begin{array}{c}-2\sqrt{\frac{2}{21}}\\\frac{5}{\sqrt{42}}\\-\frac{1}{\sqrt{42}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{2}{7}}\\-\frac{1}{\sqrt{14}}\\\frac{3}{\sqrt{14}}\\\end{array}\right)\right\}\), D)\(\left\{\left(\begin{array}{c}-\frac{3}{\sqrt{19}}\\\frac{3}{\sqrt{19}}\\-\frac{1}{\sqrt{19}}\\\end{array}\right),\left(\begin{array}{c}4\sqrt{\frac{2}{133}}\\\frac{11}{\sqrt{266}}\\\frac{9}{\sqrt{266}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{2}{7}}\\-\frac{1}{\sqrt{14}}\\\frac{3}{\sqrt{14}}\\\end{array}\right)\right\}\)
Para obter o zip que contém as instâncias deste exercício clique aqui[]
Se deseja obter o código fonte que gera os exercícios contacte miguel.dziergwa@ist.utl.pt