Chapter 3.5, Problem 37AP

To determine

(a)

To find:

The values of $k$ for which the matrix $A=\left[\begin{array}{ccc}2& k-3& k^2\\ 2& 1& 4\\ 1& k& 0\end{array}\right]$ fails to be invertible.

To determine

(b)

To find:

The volume of the parallelepiped determined by the row vectors of the matrix $A$ and column vectors of the matrix $A=\left[\begin{array}{ccc}2& k-3& k^2\\ 2& 1& 4\\ 1& k& 0\end{array}\right]$ and check whether they are equal or not.