1.

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Answer»

Solution :`[[-a^2,AB,ac],[ab,-b^2,bc],[ac,bc,-c^2]]`
=`ABC[[-a,a,a],[b,-b,b],[c,c,-c]]`0,2A,a],[0,0,b],[2c,0,-c]]` (`C_1=C_1+C_2`
`C_2=C_2+C_3`)
=`abcxx2c[[2a,a],[0,b]]`
`abcxx2c(2ab-0)`
=`4a^2b^2c^2`


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