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*n*linearly independent vectors

**x**to form a vector space

_{1},x_{2}...x_{n}*V*and use another set of

*n*linearly independent vectors

**y**to form a vector space

_{1},y_{2}...y_{n}*S*, is it necessary that

*V*and

*S*are the same? Why?

If we have a vector space

*Q*that the dimension is

*n*, can we say that any set of

*n*linearly independent vectors

**k**can form a basis of

_{1},k_{2}...k_{n}*Q*? Why?

Suppose only real numbers are involved.