Question: Example 2.11 gives a matrix that is nonsingular and is therefore associated with maps that are nonsingular. (a) Find the set of column vectors representing

Example 2.11 gives a matrix that is nonsingular and is therefore associated with maps that are nonsingular.
(a) Find the set of column vectors representing the members of the null space of any map represented by this matrix.
(b) Find the nullity of any such map.
(c) Find the set of column vectors representing the members of the range space of any map represented by this matrix.
(d) Find the rank of any such map.
(e) Check that rank plus nullity equals the dimension of the domain.

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