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Linear Algebra

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Moderate

Linearity of Projection

LINALG-L2WZXF

Suppose that $\mathcal{U}$ is a subspace of $\mathbb{R}^3$.

Also suppose that the projection of $\mathbf{x}$ onto $\mathcal{U}$ is $(1,1,0)$ and the projection of $\mathbf{y}$ onto $\mathcal{U}$ is $(1,1,-1)$.

What is the projection of $\mathbf{x} + \mathbf{y}$ onto $\mathcal{U}$?

A

$(1,1,0)$

B

$(1,1,-1)$

C

$(1,-1,0)$

D

$(2,2,-1)$

E

$(2,2,2)$