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Using properties of determinants, prove ...

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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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

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  2. Using properties of determinants, prove that: |[alpha,alpha^2,beta+gam...

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

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  4. Solve by matrix method 2/x + 3/y + 10/z = 4 , 4/x - 6/y + 5/z = 1 , ...

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  5. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  6. Let A = [[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], wher...

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  7. Fill in the blanks : If A = [(1,a,3),(2,b,6),(3,c,9)], then det A is...

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  8. Fill in the blanks : If cos 2 theta = 0, then |(0, costheta, sinthet...

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  9. Fill in the blanks : Determinant of a skew symmetric matrix of order...

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  10. Select the Correct Option If A is an invertible matrix of order 2, the...

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  11. Fill in the blanks : If A is an invertible square matrix, then (A)^-...

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  12. If A is matrix of order 3xx3, then (A^(2))^(-1)=…….

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  13. Fill in the blanks : The determinant of a diagonal matrix is equal t...

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  14. The sum of the products of elements of any row with the co-factors of ...

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  15. If A is matrix of order 3xx3, then |3A|=……….

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  16. Fill in the blanks : If A is a square matrix of order n then det (ad...

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  17. Fill in the blanks : The determinant of a triangular matrix is equal...

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  18. Find the area of the triangle whose vertices are (0,0),(a,0) and (0,b)

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  19. If A,B,C are the angles of a triangle, then Delta=|{:(sin^(2)A, cotA...

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  20. Fill in the blanks : If A is an invertible matrix of order nxxn (nge...

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