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Prove that , the value of the determin...

Prove that , the value of the determinant `|{:(x+1,x+2,x+4),(x+3,x+5,x+8),(x+7,x+10,x+14):}|` is independent of x and find the value of the determinant.

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The correct Answer is:
`(-2)`
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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. Express the square of |{:(a1,b1,0),(a2,b2,0),(a3,b3,0):}| as a third o...

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

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

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

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

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  6. |{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...

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  7. |{:(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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  8. |{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3

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

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  10. |{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...

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

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

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

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

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

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  17. |{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0

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

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

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

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