Question

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 \((0,2,-3,0,1)\).