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

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

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

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

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

Prove that {:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:} = 4abc

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)

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

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

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

Using the property of determinants and without expanding {:|( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)|:} =0

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.

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the va...

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

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

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

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  5. |{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...

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  6. |{:(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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  7. |{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3

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

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  9. |{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...

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

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

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

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

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  15. without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...

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  16. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

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  17. |{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0

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  18. if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam...

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  19. |{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" ...

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  20. Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0...

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