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Let Sb be the standard basis for R^6 . Construct a set S, which is a...

Let Sb be the standard basis for R^6 . Construct a set S, which is a subset of R^6 so that S is a basis for R^6 but S does not contain any vectors that are in Sb or any multiple of any vectors that are in Sb. Justify your claim
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Answer #1

Consider the standard basis Sb in .

Then we form the following matrix.

Hence the set

is such a set which can work for a basis of Note that S does not contain any vectors that are in Sb or any multiple of any vectors that are in Sb.

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