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show that |[y+z ,x, y],[ z+x, z, x],[x+y...

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

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

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

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

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

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

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  6. 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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  7. 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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  8. 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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  9. If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...

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

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

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

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

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

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

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  18. If the points (a1, b1),\ \ (a2, b2) and (a1+a2,\ b1+b2) are collinear,...

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  19. If the points (2,\ -3),\ (lambda,\ -1) and (0,\ 4) are collinear, find...

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  20. Using determinants, find the area of the triangle whose vertices ar...

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