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प्रश्न
Prove that `|(1/a,bc,b+c),(1/b,ca,c+a),(1/c,ab,a+b)|` = 0
उत्तर
`|(1/a,bc,b+c),(1/b,ca,c+a),(1/c,ab,a+b)|`
= `1/"abc" |(a/a,abc,a(b+c)),(b/b,abc,b(c+a)),(c/c,abc,c(a+b))|` ....(Multiply R1 by a, R2 by b, R3 by c and divide the determinant by abc)
= `"abc"/"abc" |(1,1,a(b + c)),(1,1,b(c+a)),(1,1,c(a + b))|` ....(Take out abc from C2 = 0 [∵ C1 ≡ C2])
Hence proved.
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