Question

If S is a set of 5 distinct vectors in R2, then some subset of S is a basis for R2.

Answer 1

This given statement need not be true.

Explanation -

As we know for Basis we need L.I. elements and Spanning set.

Now let a subset of S={(0,0) (1,1) (2,2) (3,3) (4,4)}

In R² with 5 distinct elements.

Now for Basis we want first - Linear independent elements but as we can see there are Linear dependent elements. So it is not Linear independent. So our first condition is failed. So it is need not be true .

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