Diferenças entre edições de "Ortogonalização e normalização"

Edição atual desde as 13h15min 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 $\mathbb{R}^3$ $\left\{\left(\begin{array}{c}-1\\-2\\-1\\\end{array}\right),\left(\begin{array}{c}-1\\1\\2\\\end{array}\right),\left(\begin{array}{c}-1\\-2\\1\\\end{array}\right)\right\}$ . Diga qual dos seguintes conjuntos corresponde á ortonormalização desta base.

A) $\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\-\sqrt{\frac{2}{3}}\\-\frac{1}{\sqrt{6}}\\\end{array}\right),\left(\begin{array}{c}-\frac{1}{\sqrt{2}}\\0\\\frac{1}{\sqrt{2}}\\\end{array}\right),\left(\begin{array}{c}\frac{1}{\sqrt{3}}\\-\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\end{array}\right)\right\}$ , B) $\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\\frac{1}{\sqrt{6}}\\\sqrt{\frac{2}{3}}\\\end{array}\right),\left(\begin{array}{c}-\frac{1}{\sqrt{2}}\\-\frac{1}{\sqrt{2}}\\0\\\end{array}\right),\left(\begin{array}{c}\frac{1}{\sqrt{3}}\\-\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\end{array}\right)\right\}$ , C) $\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\-\sqrt{\frac{2}{3}}\\\frac{1}{\sqrt{6}}\\\end{array}\right),\left(\begin{array}{c}-\frac{1}{\sqrt{30}}\\-\sqrt{\frac{2}{15}}\\-\sqrt{\frac{5}{6}}\\\end{array}\right),\left(\begin{array}{c}-\frac{2}{\sqrt{5}}\\\frac{1}{\sqrt{5}}\\0\\\end{array}\right)\right\}$ , D) $\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\-\sqrt{\frac{2}{3}}\\\frac{1}{\sqrt{6}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{5}{42}}\\4\sqrt{\frac{2}{105}}\\\frac{11}{\sqrt{210}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{5}{7}}\\\frac{1}{\sqrt{35}}\\-\frac{3}{\sqrt{35}}\\\end{array}\right)\right\}$

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

@@ Linha 16: / Linha 16: @@
 </div>
 </div>
-Considere a seguinte base de \( \mathbb{R³} \(\left\{\left(\begin{array}{c}3\\1\\-1\\\end{array}\right),\left(\begin{array}{c}1\\0\\0\\\end{array}\right),\left(\begin{array}{c}-2\\-1\\0\\\end{array}\right)\right\}\)Diga qual dos seguintes conjuntos corresponde á ortonormalização desta base.
+Considere a seguinte base de \( \mathbb{R}^3 \) \(\left\{\left(\begin{array}{c}-1\\-2\\-1\\\end{array}\right),\left(\begin{array}{c}-1\\1\\2\\\end{array}\right),\left(\begin{array}{c}-1\\-2\\1\\\end{array}\right)\right\}\). Diga qual dos seguintes conjuntos corresponde á ortonormalização desta base.
-A)\(\left(\begin{array}{ccc}\frac{1}{\sqrt{3}}&#038;\frac{1}{\sqrt{3}}&#038;-\frac{1}{\sqrt{3}}\\0&#038;-\frac{1}{\sqrt{2}}&#038;-\frac{1}{\sqrt{2}}\\-\sqrt{\frac{2}{3}}&#038;\frac{1}{\sqrt{6}}&#038;-\frac{1}{\sqrt{6}}\\\end{array}\right)\),
+A)\(\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\-\sqrt{\frac{2}{3}}\\-\frac{1}{\sqrt{6}}\\\end{array}\right),\left(\begin{array}{c}-\frac{1}{\sqrt{2}}\\0\\\frac{1}{\sqrt{2}}\\\end{array}\right),\left(\begin{array}{c}\frac{1}{\sqrt{3}}\\-\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\end{array}\right)\right\}\),
-B)\(\left(\begin{array}{ccc}\frac{1}{\sqrt{3}}&#038;\frac{1}{\sqrt{3}}&#038;-\frac{1}{\sqrt{3}}\\-\frac{7}{\sqrt{78}}&#038;\sqrt{\frac{2}{39}}&#038;-\frac{5}{\sqrt{78}}\\\frac{1}{\sqrt{26}}&#038;-2\sqrt{\frac{2}{13}}&#038;-\frac{3}{\sqrt{26}}\\\end{array}\right)\),
+B)\(\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\\frac{1}{\sqrt{6}}\\\sqrt{\frac{2}{3}}\\\end{array}\right),\left(\begin{array}{c}-\frac{1}{\sqrt{2}}\\-\frac{1}{\sqrt{2}}\\0\\\end{array}\right),\left(\begin{array}{c}\frac{1}{\sqrt{3}}\\-\frac{1}{\sqrt{3}}\\\frac{1}{\sqrt{3}}\\\end{array}\right)\right\}\),
-C)\(\left(\begin{array}{ccc}-\frac{2}{3}&#038;\frac{1}{3}&#038;-\frac{2}{3}\\\frac{11}{3\sqrt{26}}&#038;\frac{4\sqrt{\frac{2}{13}}}{3}&#038;-\frac{7}{3\sqrt{26}}\\\frac{1}{\sqrt{26}}&#038;-2\sqrt{\frac{2}{13}}&#038;-\frac{3}{\sqrt{26}}\\\end{array}\right)\),
+C)\(\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\-\sqrt{\frac{2}{3}}\\\frac{1}{\sqrt{6}}\\\end{array}\right),\left(\begin{array}{c}-\frac{1}{\sqrt{30}}\\-\sqrt{\frac{2}{15}}\\-\sqrt{\frac{5}{6}}\\\end{array}\right),\left(\begin{array}{c}-\frac{2}{\sqrt{5}}\\\frac{1}{\sqrt{5}}\\0\\\end{array}\right)\right\}\),
-D)\(\left(\begin{array}{ccc}0&#038;-\frac{1}{\sqrt{2}}&#038;-\frac{1}{\sqrt{2}}\\-2\sqrt{\frac{2}{17}}&#038;\frac{3}{\sqrt{34}}&#038;-\frac{3}{\sqrt{34}}\\\frac{3}{\sqrt{17}}&#038;\frac{2}{\sqrt{17}}&#038;-\frac{2}{\sqrt{17}}\\\end{array}\right)\)
+D)\(\left\{\left(\begin{array}{c}-\frac{1}{\sqrt{6}}\\-\sqrt{\frac{2}{3}}\\\frac{1}{\sqrt{6}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{5}{42}}\\4\sqrt{\frac{2}{105}}\\\frac{11}{\sqrt{210}}\\\end{array}\right),\left(\begin{array}{c}-\sqrt{\frac{5}{7}}\\\frac{1}{\sqrt{35}}\\-\frac{3}{\sqrt{35}}\\\end{array}\right)\right\}\)
-Para obter o zip que contém as instâncias deste exercício clique aqui[]
+Para obter o zip que contém as instâncias deste exercício clique aqui[https://drive.tecnico.ulisboa.pt/download/1695923671436179/instanciasGramSchmidt.zip]
 Se deseja obter o código fonte que gera os exercícios contacte miguel.dziergwa@ist.utl.pt

Diferenças entre edições de "Ortogonalização e normalização"

Edição atual desde as 13h15min de 28 de julho de 2016

Menu de navegação

Pesquisa