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## Homework Statement

a) If U and W are subspaces of R^3, show that it is possible to find a basis B for R^3 such that one subset of B is a basis for U and another subset of B (possibly overlapping) is a basis for W.

b) If U and W are subspaces of a finite-dimensional vector space V, show that it is possible to find a basis for V such that one subset of that basis is a basis for U and another subset of that basis (possibly overlapping) is a basis for W.

## Homework Equations

none really

## The Attempt at a Solution

B = ( v_1, v_2, v_3 ), such that these vectors are a basis for V.

Then:

V = t_1*v_1 + t_2*v_2 + t_3*v_3

...stuck here