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A-M-2016-2016-with-the-entries-a-ij-0-if-i-j-2016-1-if-i-j-2016-find-the-determinant-




Question Number 11958 by 7991 last updated on 07/Apr/17
A∈M_(2016×2016)    with the entries a_(ij) {_(0, if i+j≠2016) ^(1, if i+j=2016)   find the determinant??
$${A}\in{M}_{\mathrm{2016}×\mathrm{2016}} \: \\ $$$${with}\:{the}\:{entries}\:{a}_{{ij}} \left\{_{\mathrm{0},\:{if}\:{i}+{j}\neq\mathrm{2016}} ^{\mathrm{1},\:{if}\:{i}+{j}=\mathrm{2016}} \right. \\ $$$${find}\:{the}\:{determinant}?? \\ $$
Commented by prakash jain last updated on 08/Apr/17
Row 2016 is all 0s.  Hence determinant =0.
$$\mathrm{Row}\:\mathrm{2016}\:\mathrm{is}\:\mathrm{all}\:\mathrm{0s}. \\ $$$$\mathrm{Hence}\:\mathrm{determinant}\:=\mathrm{0}. \\ $$

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