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|{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|...

`|{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|`

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The correct Answer is:
`(a+b+c)(c-a)^2`
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|{:(a,b,c),(b,c,a),(c,a,b):}|

|{:(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c):}|=3abc-a^3-b^3-c^3

|{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|

|{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc

If omega is an imaginary cube root of unity , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a+b+c)(a+bomega+comega^2)(a+bomega^2+comega)

If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0, then show that either a+b+c=0 or, a=b=c.

If |{:(a,b,1),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,bc),(b-c,b-a,ca):}|-|{:(c-a,c-b,c^(2)),(a-b,a-c,a^(2)),(b-c,b-a,b^(2)):}|=p , then the number of positive divisors of p is

|{:(-1,b,c),(a,-1,c),(a,b,-1):}|=(a+1)(b+1)(c+1)((a)/(a+1)+(b)/(b+1)+(c)/(c+1)-1)

If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(c,a,b),(b,c,a)| , then the value of k, is 1 b. 2 c. 3 d. 4

Show that, |{:(" "a,b-c,c+b),(a+c," "b,c-a),(a-b,b+a," "c):}|=(a+b+c)(a^2+b^2+c^2)

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. |{:((b+c)^2," "a^2," "a^2),(" "b^2,(c+a)^2," "b^2),(" "c^2," "c^2,(...

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  2. Factorise : |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|

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  3. |{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|

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  4. If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , p...

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  5. Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}|, hence show that . |{:(0,c,b)...

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  6. Express the square of |{:(a1,b1,0),(a2,b2,0),(a3,b3,0):}| as a third o...

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  7. prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the va...

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  8. Prove that , the value of the determinant |{:(x+1,x+2,x+4),(x+3,x+5,...

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  9. |{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc

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  10. |{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2...

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  11. |{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...

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  12. |{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)

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  13. |{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3

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  14. |{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...

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  15. |{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...

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  16. |{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...

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  17. |{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0...

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  18. prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,...

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  19. If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+...

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  20. If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...

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