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If A=|[a, b, c],[ x, y, z],[ p, q, r]| ...

If `A=|[a, b, c],[ x, y, z],[ p, q, r]|` and `B=|[q, -b, y],[ -p, a, -x],[ r,-c, z]|` , without expanding or evaluating `A` and `B` , show that `A+B=0` .

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
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  2. Let D=|Ax x^2 1 By y^2 1 Cz z^2 1| and D1=|A B C x y z yz zx xy| ...

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  3. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

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  11. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

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  12. Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,g...

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  13. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

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  14. In a A B C ,if|1 1 1 1+cosA 1+cosB 1+cosC cos^2A+A cos^2B+cosB cos^2...

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  16. If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove th...

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  17. For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z...

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  18. Using properties of determinants, show that |1 a a^2 -b c 1 b ...

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