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Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( ...

Prove: `|(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3`

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If A=|(1,1,1),(a,b,c),(a^3,b^3,c^3)|, B=|(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3)|, C=|(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)| , then which relation is correct :

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

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

Using the properties of determinants, prove that following |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

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

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

Prove that: |(-2a , a+b, a+c),( b+a,-2b, b+c),( c+a , c+b,-2c)|=4(a+b)(b+c)(c+a)

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^3

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

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  2. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

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  3. Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

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

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  5. Prove: |(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a ...

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  6. By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...

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  7. show that |{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}|=k^(2)(3y+k)

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  8. Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

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  9. Show that | (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a...

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  10. Prove: |(1+a,1, 1),( 1, 1+a, 1),(1, 1, 1+a)|=a^3 +3a^2

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  11. Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

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  12. show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

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  13. Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z)...

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  14. Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)...

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  15. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

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  16. Show that |[x+1,x+2,x+a], [x+2,x+3,x+b],[ x+3,x+4,x+c]|=0 where a ,\ b...

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  17. Show that [[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]=0 whe...

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  18. If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...

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  19. a!=p , b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 the value of p/(p-...

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  20. Show that x=2 is a root of the equation |(x,-6,-1),( 2,-3x,x-3),(-3,...

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