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

Show that `| (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a^2 - b^2), 2c^3), (2a^3, 2b^3, -c(a^2 + b^2 - C^2))|` = abc`(a^2 + b^2 + c^2)^3`

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

Factorise : 2ab^(2) c - 2a + 3b^(3) c - 3b - 4b^(2) c^(2) + 4c

Prove that a(b^(2) + c^(2)) cos A + b(c^(2) + a^(2)) cos B + c(a^(2) + b^(2)) cos C = 3abc

Factorise : 12abc -6a^(2) b^(2) c^(2) + 3a^(3) b^(3) c^(3)

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

Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a b+b c+c a) .

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

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 b,-a b)|=(a b+b c+c a)^3

Show that: |[a, a+b ,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]|=a^3 .

Factorize : (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. show that |{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}|=k^(2)(3y+k)

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

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

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

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

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

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

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

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  9. 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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  10. 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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  11. 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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  12. If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...

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

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  15. Solve the following determinant equation: |[x+a, b, c], [c, x+b, a],...

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  16. Solve the following: |[x+1, 3, 5], [2,x+2, 5], [2, 3,x+4]|=0

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  17. Solve the following: |[1, 1,x], [p+1,p+1,p+x],[3,x+1,x+2]|=0

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  18. If a ,b and c are all non-zero and |(1+a,1,1),( 1,1+b,1),(1,1,1+c)|=...

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  19. Find the area of the triangle with vertices A\ (5,\ 4),\ \ B(-2,\ 4...

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  20. Show that pointsA (a , b + c), B (b , c + a), C (c , a + b)are collin...

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