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Prove: |(y+z, z, y),( z, z+x,x),( y, x,x...

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

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prove that: |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

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

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

Using properties of determinants, prove that |{:(y + z ,z + x ,x + y ),(z + x ,x + y ,y + z),(x + y ,y + z,z + x ):}|=2 |{:(x, y, z),(y, z, x),(z, x, y):}|= - 2 (x^(3) + y^(3) + z^(3) - 3xyz)

Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+z+2y):}|=2(x+y+z)^(3)

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)

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Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...

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

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

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

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

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

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

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

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

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  10. 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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  11. 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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  12. 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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  13. If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...

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

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

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

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

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

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