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

anjali agarwal Grade: 12

        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

7 years ago

Answers : (1)

Askiitians Expert Sahil Arora - IITD

19 Points

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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Sahil Arora
IIT Delhi

7 years ago

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