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

Prove:`\ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Evaluate the following: |[0,x y^2,x z^2],[x^2y,0,y z^2],[x^2z, z y^2,...

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  2. If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"1=|(1, 1, 1),(...

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  3. Prove:\ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

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  4. Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^...

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  5. Prove: |(a+b,b+c,c+a),( b+c,c+a, a+b),( c+a, a+b,b+c)|=2|(a, b, c),( b...

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  6. Prove: |[a+b+2c, a, b], [c, b+c+2a, b], [c ,a ,c+a+2b]|=2(a+b+c)^3

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  7. Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  8. 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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  9. 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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  10. Find dy/dx if x-y+x^5=sinx

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  11. Prove: |(z, x, y),( z^2,x^2,y^2),(z^4,x^4,y^4)|=|(x, y, z),( x^2,y^2,z...

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

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  13. Prove: |((a+1)(a+2),(a+2),1 ),((a+2)(a+3),(a+3),1), ((a+3)(a+4) ,(a+4)...

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

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  15. Prove: |[1,a^2+bc, a^3],[ 1,b^2+c a, b^3],[ 1,c^2+a b, c^3]|=-(a-b)(b-...

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

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

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  19. 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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  20. Prove: |[a^2, 2ab,b^2],[b^2,a^2, 2ab],[2ab,b^2,a^2]|=(a^3+b^3)^2

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