Question

The determinant of the matrix $$\left[\begin{array}{cccc}6& -8& 1& 1\\ 0& 2& 4& 6\\ 0& 0& 4& 8\\ 0& 0& 0& -1\end{array}\right]$$

• A. 11
• B. - 48
• C. 0
• D. - 24

Answer 1

The correct option is B - 48

Given $A=\left[\begin{array}{cccc}6& -8& 1& 1\\ 0& 2& 4& 6\\ 0& 0& 4& 8\\ 0& 0& 0& -1\end{array}\right]$
$\Rightarrow$ it is upper triangular matrix.
$\Rightarrow$ The determinant of an upper triangular matrix is equal to product of its diagonal elements
i.e. $\left|A\right|$=$\prod a_{ii}=a_{11}.a_{22}.a_{33}.a_{44}$
$=6\times 2\times 4\times \times (-1)=-48$