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determinant-0-4-1-1-4-0-0-1-3-5-2-1-2-2-5-1-




Question Number 169702 by Anyangwa last updated on 06/May/22
 determinant ((0,4,1,1),(4,0,0,1),(3,5,2,1),(2,2,5,1))=
$$\begin{vmatrix}{\mathrm{0}}&{\mathrm{4}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{4}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{3}}&{\mathrm{5}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{2}}&{\mathrm{2}}&{\mathrm{5}}&{\mathrm{1}}\end{vmatrix}=\: \\ $$
Answered by MikeH last updated on 06/May/22
Identify the row with maximum number  of zeros.  −4(4(2−5)+(15−4))+(4(5−2)−0+(6−10)  (4(25−4)) = −72
$$\mathrm{Identify}\:\mathrm{the}\:\mathrm{row}\:\mathrm{with}\:\mathrm{maximum}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{zeros}. \\ $$$$−\mathrm{4}\left(\mathrm{4}\left(\mathrm{2}−\mathrm{5}\right)+\left(\mathrm{15}−\mathrm{4}\right)\right)+\left(\mathrm{4}\left(\mathrm{5}−\mathrm{2}\right)−\mathrm{0}+\left(\mathrm{6}−\mathrm{10}\right)\right. \\ $$$$\left(\mathrm{4}\left(\mathrm{25}−\mathrm{4}\right)\right)\:=\:−\mathrm{72} \\ $$

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