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Linear algebra

Show that the set of all elements of R^3 of the form (a + b, -a, 2b), where a and b are any real numbers, is a subspace of R^3. Show that the geometric interpretation of this subspace is a plane and find its equation.

Solution Preview

The set V = {(a+b, -a, 2b): a, b are real numbers} is closed with respect to addition and multiplication by scalar since:
<br>(1) (a+b, -a, 2b) + (c+d, -c, 2d) = (a+c+b+d, -(a+c), 2(b+d))
<br>and (2) ...