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Prove that: |b c-a^2c a-b^2a b-c^2c a-b^...

Prove that: `|b c-a^2c a-b^2a b-c^2c a-b^2a b-c^2b c-a^2a b-c^2b c-a^2c a-b^2|` is divisible by `a+b+c` and find the quotient.

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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
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  6. If "Delta"r=|2^(r-1)2. 3^(r-1)4. 5^(r-1)x y z2^n-1 3^n-1 5^n-1|dot Sho...

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  7. If m is a positive integer and Dr=|(2r-1,\ ^m Cr,1),(m^2-1, 2^m ,m+1...

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  8. Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b,...

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  9. Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y...

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  10. Prove that: |-2a a+b a+c b+a-2bb+cc+a c+b-2c|=4(a+b)(b+c)(c+a)

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  11. Without expanding, show that the value of each of the following det...

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  12. Prove: |(1,b+c ,b^2+c^2),( 1,c+a ,c^2+a^2),( 1,a+b ,a^2+b^2)|=(a-b)(b-...

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  13. Prove: |(a, a+b, a+2b),( a+2b, a ,a+b ),(a+b, a+2b, a)|=9(a+b)b^2

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  14. Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c...

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  15. Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b...

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  16. Prove: |(x+4,x,x),(x,x+4,x),(x,x,x+4)|=16(3x+4)

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  17. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=

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  18. Prove: |(a, b-c,c-b),( a-c, b, c-a),( a-b,b-a, c)|=(a+b-c)(b+c-a)(c+a-...

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  19. Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

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  20. Prove: |1a a^2a^2 1a a a^2 1|=(a^3-1)^2

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