###### Exercise 5

For each of the following conditions, construct a \(3\times 3\) matrix having the given properties.

\(\dim~\nul(A) = 0\text{.}\)

\(\dim~\nul(A) = 1\text{.}\)

\(\dim~\nul(A) = 2\text{.}\)

\(\dim~\nul(A) = 3\text{.}\)

For each of the following conditions, construct a \(3\times 3\) matrix having the given properties.

\(\dim~\nul(A) = 0\text{.}\)

\(\dim~\nul(A) = 1\text{.}\)

\(\dim~\nul(A) = 2\text{.}\)

\(\dim~\nul(A) = 3\text{.}\)