Question

The determinant of the given matrix,
$A=\left[\begin{array}{cccc}21& 17& 7& 10\\ 24& 22& 6& 10\\ 6& 8& 2& 3\\ 5& 7& 1& 2\end{array}\right]willbe$ ___________

• A. 442
• B. 0
• C. 1
• D. None of the above

Answer 1

The correct option is B 0

$GivenmatrixA=\left[\begin{array}{cccc}21& 17& 7& 10\\ 24& 22& 6& 10\\ 6& 8& 2& 3\\ 5& 7& 1& 2\end{array}\right]$

$Operating,R_1\to R_1-R_2-R_4,R_2\to R_2-3R_3$
$and{R}_3\to R_3-2R_4$

$A=\left[\begin{array}{cccc}-8& -12& 0& -2\\ 6& -2& 0& 1\\ -4& -6& 0& -1\\ 5& 7& 1& 2\end{array}\right]$

$|A|=-\left[\begin{array}{ccc}-8& -12& -2\\ 6& -2& 1\\ -4& -6& -1\end{array}\right]=0$