Question: Prove or disprove if the following are vector subspaces The set {(x, y, z) R 3 | x + y = 0} R 3 .

Prove or disprove if the following are vector subspaces

The set {(x, y, z) R 3 | x + y = 0} R 3 .

The set of all 22 matrices of determinant 0, as a subset of M22.

The set of continuous functions f : R R satisfying R 3 1 f(x) dx = 0, as a subset of C0.

The set of all polynomials p(x) such that p(1)p(4) = 0, as a subset of P.

I understand you have to show they are closed under addition, scalar multiplication and contain the zero vector but I'm not sure how to show those

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