Question: Use the definition of projection, as stated here, for problems a to b A linear transformation T: V W, where W is a sub-space

Use the definition of projection, as stated here, for problems a to b
A linear transformation T: V → W, where W is a sub-space of V, is called a projection provided that T, when restricted to W, reduces to the identity mapping; that is
For all vectors w in the subspace W.
a. Verify that the transformation in Example 1 is a projection. What is W in this case?
b. Verify that the transformation in Example 2 is a projection. What is W in this case?

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