Projecting to the range of a matrix

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Homework Statement



Let U = span({(1, 2, 1)t, (1, 0, 0)t}) and V = span({(0, 1, 1)t}) be subspaces of
R3. Find the matrix B representing the projection onto V parallel to U.

Homework Equations





The Attempt at a Solution



If a matrix C with range U and and a matrix D whose nullspace is V then we can find the projection of matrix B

B = C(DC)−1D

Is my thought correct?
 
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