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Question Number 9287 by suci last updated on 28/Nov/16 | ||
$${find}\:{the}\:{determinant}\:{of}\:{the}\:{matrix}\:{below} \\ $$$$\begin{vmatrix}{\mathrm{0}}&{\mathrm{4}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{2}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{5}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\end{vmatrix} \\ $$ | ||
Answered by mrW last updated on 28/Nov/16 | ||
$$=−\mathrm{4}×\begin{vmatrix}{\mathrm{0}}&{\mathrm{0}}&{\mathrm{2}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{5}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\end{vmatrix} \\ $$$$=−\mathrm{4}×\mathrm{2}×\begin{vmatrix}{\mathrm{0}}&{\mathrm{3}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{5}}&{\mathrm{0}}&{\mathrm{0}}\end{vmatrix} \\ $$$$=−\mathrm{4}×\mathrm{2}×\left(−\mathrm{3}\right)×\begin{vmatrix}{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{5}}&{\mathrm{0}}\end{vmatrix} \\ $$$$=−\mathrm{4}×\mathrm{2}×\left(−\mathrm{3}\right)×\left(−\mathrm{5}×\mathrm{1}\right) \\ $$$$=−\mathrm{120} \\ $$ | ||
Answered by mrW last updated on 28/Nov/16 | ||
$$\mathrm{or} \\ $$$$=−\begin{vmatrix}{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{2}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{4}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{5}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\end{vmatrix} \\ $$$$=−\mathrm{120} \\ $$ | ||