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Compute the dimension and find bases for the following linear spaces.

a) Real anti-symmetric $4 \times 4$ matrices.
b) Quartic polynomials $p$ with the property that $p(2)=0$ and $p(3)=0$.
c) Cubic polynomials $p(x, y)$ in two real variables with the properties: $p(0,0)=0$, $p(1,0)=0$ and $p(0,1)=0 .$
d) The space of linear maps $L: \mathbb{R}^{5} \rightarrow \mathbb{R}^{3}$ whose kernels contain $(0,2,-3,0,1)$.
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