Question

show that if {u,v} , u not = v is a basis for V then { u + v, an}, a not= basis for V

Answer 1

Answer:

We have to prove that the point r = xi + yj can be expressed in the form Uu + Vv.

In other words in the form Mm, where M is the 2×2 matrix whose elements are the coordinates of u and v, and m is (U, V).

Yes, this is possible, and m is simply M⁻¹r.

We know that M⁻¹ exists because M is non-singular because u and v are linearly independent vectors.

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