/ 029 - Esses três vetores Esses três vetores (#a, #b, #c) (#d, #e, #f) (#g, #h, #i) são uma base em «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math»?

{#1}

]]> Quando estes três vetores (#a, #b, #c) (#d, #e, #f) (#g, #h, #i) formam uma base para o espaço «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math», significa que todo vetor no espaço «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math»pode ser escrito como uma combinação linear desse vetores.

Para que isso seja verdadeiro, é necessário que esses vetores sejam linearmente independentes.

Três vetores são linearmente independentes se, e somente se, o determinante da matriz formada por suas coordenadas for diferente de zero.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»d«/mi»«mi»e«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»§#913;«/mi»«mo»=«/mo»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»b«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»d«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»e«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»f«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»g«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»h«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»i«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»r«/mi»«mo».«/mo»«/math».

Portanto; #certo para o espaço «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«/math».

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