Past exam of the mathematical methods I course of the University of Oxford / 2015 resit / 7 / iii

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- Solution iii

Solution

No. Calling the three vectors

v_{1}, v_{2}, v_{3}

in order, direct addition gives

v_{3} = v_{1} + v_{2}

. This nontrivial linear dependence prevents them from forming a basis of

R^{3}

. The first two are not proportional, so the span has dimension two.

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