Chapter 3.5, Problem 6AP

To determine

(a)

To evaluate:

The determinant of the matrix $A=\left[\begin{array}{cccc}3& -1& -2& 1\\ 0& 0& 1& 4\\ 0& 2& 1& -1\\ 0& 0& 0& -4\end{array}\right]$ by using the definition $\mathrm{3.1.8}$.

To determine

(b)

To evaluate:

The determinant of the matrix $A=\left[\begin{array}{cccc}3& -1& -2& 1\\ 0& 0& 1& 4\\ 0& 2& 1& -1\\ 0& 0& 0& -4\end{array}\right]$ by using elementary row operations to reduce A to an upper triangular matrix.

To determine

(c)

To evaluate:

The determinant of the matrix $A=\left[\begin{array}{cccc}3& -1& -2& 1\\ 0& 0& 1& 4\\ 0& 2& 1& -1\\ 0& 0& 0& -4\end{array}\right]$ by using the Cofactor Expansion Theorem.