Home
Class 12
MATHS
Using properties of determinants, prove...

Using properties of determinants, prove the following: `|[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2`

Text Solution

Verified by Experts

`L.H.S. = |[1,x,x^2],[x^2,1,x],[x,x^2,1]|`
Applying `C_1->C_1-xC_3`
`= |[1-x^3,x,x^2],[0,1,x],[0,x^2,1]|`
Expanding by columns,
`=(1-x^3)(1-x^3) -0+0`
`=(1-x^3)^2 = R.H.S.`
Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Using properties of determinants, prove the following: |[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 properties of determinant prove 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: det[[1,x,x^(2)x^(2),1,xx,x^(2),1]]=(1-x^(3))^(2)

Prove det[[1,x,x^(2)x^(2),1,xx,x^(2),1]]=(1-x^(3))^(2)

By using properties of determinants, prove that the determinant |(a,sin x,cos x),(-sin x,-a,1),(cos x,1,a)| is independent of x.

Find the sum to n terms of the following series: (x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+(x^(3)+(1)/(x^(3)))^(2)+(x^(4)+(1)/(x^(4)))^(2)+

Prove that |[x^2,2x,1],[1,x^2,2x] , [2x,1,x^2]| is a perfect square

solve for x, [[x^2,1],[2,x]] + [[2x,2],[-1,2]] = [[-1,3],[1,1]]

Simplify each of the following 2x^(2) + 3x (1 -2x^(3)) + x(x + 1)

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. If a matrix has 5 elements, write all possible orders it can have.

    Text Solution

    |

  2. If A=[[2, 3],[ 5,-2]], write A^(-1) in terms of A

    Text Solution

    |

  3. Using properties of determinants, prove the following: |[1,x,x^2],[...

    Text Solution

    |

  4. Write the projection of the vector hat i- hat j on the vector ha...

    Text Solution

    |

  5. Write the direction-cosines of the line joining the points (1, 0, 0...

    Text Solution

    |

  6. Differentiate the following function with respect to x : (log\ x)^...

    Text Solution

    |

  7. If y=log[x+sqrt(x^2+a^2)\ ] , show that ((x^2+a^2)(d^2\ y)/(dx^2)+x(dy...

    Text Solution

    |

  8. Evaluate: int0^(pi/4)(cos^2x)/(cos^2x+4sin^2x)dx\

    Text Solution

    |

  9. Evaluate: int1^3(x^2+x)dx

    Text Solution

    |

  10. Show that of all the rectangles inscribed in a given fixed circle, ...

    Text Solution

    |

  11. Using integration find the area of the triangular region whose side...

    Text Solution

    |

  12. Show that the function f in A=|R-{2/3}\ defined as f(x)=(4x+3)/(6x-4)...

    Text Solution

    |

  13. Find the equation of the plane which contains the line of intersect...

    Text Solution

    |

  14. Find a unit vector perpendicular to each of the vector vec a+ vec ...

    Text Solution

    |

  15. Find the angle between the following pair of lines: (-x+2)/(-2)=(y-...

    Text Solution

    |

  16. Probabilities of solving a specific problem independently by A and ...

    Text Solution

    |

  17. If x=a^s in^((-1))\ t ,\ y=a^cos^((-1))t ,\ show that (dy)/(dx)=-y/x

    Text Solution

    |

  18. Find the points on the curve y=x^3 at which the slope of the tangen...

    Text Solution

    |

  19. Find the intervals in which the function f given by f(x)=sinx+cosx ,\...

    Text Solution

    |

  20. A factory makes tennis rackets and cricket bats. A tennis racket ta...

    Text Solution

    |