Find two different bases for which both contain the vectors and .

Let

Then and are both bases of (it is sufficient to show they are linearly independent sets, which can be readily checked). They also both contain the requested vectors.

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Stumbling Robot

A Fraction of a Dot
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Find two bases of *R*^{4} which both contain *(0,1,1,1), (1,1,1,1)*

Find two different bases for which both contain the vectors and .

Let

Then and are both bases of (it is sufficient to show they are linearly independent sets, which can be readily checked). They also both contain the requested vectors.