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

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`

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

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

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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

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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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

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  2. 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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  3. 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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  4. By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...

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

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. 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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  16. If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...

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

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

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

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