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my question is that: without expanding prove that: 0 99 -998 -99 0 997 998 -997 0 =0. i.e the determinant of above matrix is zero

my question is that:


without expanding prove that:


0    99   -998


-99   0  997


998  -997  0


=0.


i.e the determinant of above matrix is zero


 

Grade:12

1 Answers

Askiitians Expert Sahil Arora - IITD
19 Points
11 years ago

Dear anjali

Let A=

0    99   -998

-99   0  997

998  -997  0

then Its transpose=

0    -99   998

99   0  -997

-998  997  0

add A and its transpose

we get a zero matrix......

so u get A+its transpose= 0 matrix.....

since |A|=|transpose of  A|

==>|A|=0

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All the best anjali !!!




Regards,

Askiitians Experts

Sahil Arora
IIT Delhi

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