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प्रश्न
Prove that `|(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)| = 4a^2b^2c^2`
उत्तर
`|(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|`
= `abc|(-a,b,c),(a,-b,c),(a,b,-c)|` ....(Take out a,b,c respectively from R1, R2 and R3)
= `a^2b^2c^2 |(-1,1,1),(1,-1,1),(1,1,-1)|` ...(Take out a,b,c respectively from C1, C2 and C3)
= `a^2b^2c^2 |(-1,1,1),(0,0,2),(0,2,0)|` ...`[("R"_2 -> "R"_2 + "R"_1),("R"_3 -> "R"_3 + "R"_1)]`
= a2b2c2 [-(0 – 4) + 0 + 0]
= 4a2b2c2
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