Identify which of the following sets form a subspace and which do not. Justify your claim. Then find a basis for each subspace.

a. S1 ≡ the set of all polynomials with degrees less than 3.

b. S2 ≡ {y(x)|y ′′ + 2y + 3 = x 2}.

c. S3 ≡ the set of all 2 × 2 anti-symmetric matrices.

d. S4 ≡ the set of all 3 × 3 matrices with a non-zero eigenvalue.

e. S5 ≡ the set of all 3 × 3 matrices with a zero eigenvalue.

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