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Using properties of determinants, prove that: `|[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)`

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ACCURATE PUBLICATION-DETERMINANTS-(Question carrying 2 marks)
  1. If Delta=|{:(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1):}|"...

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  2. Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,...

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  3. Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b...

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  4. If a, b, c are positive and unequal, show that value of the determinan...

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  5. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

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  6. Using properties of determinant , show that : |{:(a,b,c),(a^(2),b^(2...

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  7. Prove that |{:((a+1)(a+2),a+2,1),((a+2)(a+3),a+3,1),((a+3)(a+4),a+4,1)...

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  8. Without expanding, prove the following |(a,a+b,a+2b),(a+2b,a,a+b),(...

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  9. Prove that: {:|(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+b^2,2a),(2b,-2a,1-a^2-...

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  10. Prove that |{:(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b...

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  11. Without expanding, prove the following |(a,b-c,c-b),(a-c,b,c-a),(a-...

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  12. If a+b+c ne 0 and |{:(a,b,c),(b,c,a),(c,a,b):}|=0, then using properti...

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  13. Using the properties of determinants, prove that following : |{:(1,x...

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  14. If f(x) = {:|(a,-1,0),(ax,a,-1),(ax^2,ax,a)|, using properties of dete...

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  15. Show that triangle = |[(y+z)^2,xy,zx],[xy,(x+z)^2,yz],[xz,yz,(x+y)^2]|...

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  16. If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}| and Delta(1)=|{:(1,...

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  17. Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1...

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  18. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

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  19. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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  20. For the matrix A=[{:(3,2),(1,1):}], find the numbers a and b such that...

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