Statistics Solutions

Solution: (a) Show that the null space of the matrix (lll0 1 0 , 1 0 0 , 0 0 0) is the z -axis in R^3 and its column space is the xy-plane. (b) Find a 3

Question: (a) Show that the null space of the matrix \(\left(\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0\end{array}\right)\) is the \(z\) -axis in \(\mathbb{R}^{3}\) and its column space is the xy-plane.

(b) Find a \(3 \times 3\) matrix whose null space is the \(x\) -axis and whose column space is the yz-plane.

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