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By using properties of determinants, sh...

By using properties of determinants, show that : `|[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2`

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By using properties of determinants, show that : |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]| = (5x+4)(4-x)^2

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

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)

Using the properties of determinant, show that : |[1,x+y,x^2+y^2],[1,y+z,y^2+z^2],[1,z+x,z^2+x^2]| = (x-y)(y-z)(z-x)

By using properties of determinants, show that |{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(4-x)^(2)

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Using the properties of determinants, prove that following : |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1)):}|=6x^(2)(1-x^(2))

Using the properties of determinants, find the value of x, if: {:|(x+2,x+6,x-1),(x+6,x-1,x+2),(x-1,x+2,x+6)|=0

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^(3)...

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  2. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

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

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  4. 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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  5. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  6. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  7. Which of the following is correct

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  8. Find area of the triangle with vertices at the point given in the fol...

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  9. Find area of the triangle with vertices at the point given in the fol...

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  10. Find area of the triangle with vertices at the point given in the fol...

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  11. Show that points : A (a,b+c),B(b,c+a),C(c,a+b) are collinear.

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  12. Find the value of k if the area of the triangle is 4 sq. units whose v...

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  13. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  14. Find equation of line joining (1, 2) and (3, 6) using determinants.

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  15. Find equation of line joining (3, 1) and (9, 3) using determinants.

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  16. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

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  17. Write Minors and Cofactors of the elements of following determinant : ...

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  18. Write Minors and Cofactors of the elements of following determinant : ...

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  19. Write Minors and Cofactors of the elements of following determinant : ...

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  20. Write Minors and Cofactors of the elements of following determinant : ...

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