Home
Class 12
MATHS
By using properties of determinants, pro...

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

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BODY BOOKS PUBLICATION|Exercise EXERCISE|148 Videos

  • DIFFERENTIAL EQUATIONS

    BODY BOOKS PUBLICATION|Exercise EXERCISE|5 Videos

Similar Questions

Explore conceptually related problems

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

Using properties of determinants prove the following. abs[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

solve using properties of determinants. abs[[2x-1,x+7,x+4],[x,6,2],[x-1,x+1,3]]=0

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

The coefficient of x^(2) in the expansion of the determinant |(x^(2) , x^(3) +1, x^(5)+2),(x^(3)+3, x^(2)+x, x^(3)+x^(4)),(x+4,x^(3)+x^(4),2^(3))| is a) -10 b) -8 c) -2 d) -6

Prove that cos^2 2x-cos^2 6x=sin4x sin8x

The maximum degree of x by which determinant |(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)| divisible is a)0 b)1 c)2 d)3

The value of the determinant |(x+2,x+3,x+5),(x+4,x+6,x+9),(x+8,x+11,x+15)| is A)2 B)-2 C)3 D)-1

If x=(1+i)/sqrt2 .Prove that x^6+x^4+x^2+1=0

Verify Rolle's Theorem for the function f(x)=x^2+2x-8 , x in [-4,2]

BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that abs[[1!,2!,3!],[2!,3!,4!],[3!,4!,5!]]=4!

    Text Solution

    |

  2. Solve the system of Linear equations x+2y+z=8,2x+y-z=1,x-y+z=2

    Text Solution

    |

  3. Inverse of the matrix [[0,1,2],[0,1,1],[1,0,2]]

    Text Solution

    |

  4. Find the values of x in which abs[[3,x],[x,1]]=abs[[3,2],[4,1]]

    Text Solution

    |

  5. Using the property of determinants,show that the points A(a,b+c),B(b...

    Text Solution

    |

  6. Examine the consistency of system of following equations: 5x-6y+4z...

    Text Solution

    |

  7. Let B is a square matrix of order 5, then abs[kB] is equal to….

    Text Solution

    |

  8. Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

    Text Solution

    |

  9. Check the consistency of the following equations, 2x+3y+z=6,x+2y-z...

    Text Solution

    |

  10. If abs[[x,3],[5,2]]=5,then x=…..

    Text Solution

    |

  11. By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],...

    Text Solution

    |

  12. Solve the following system of linear Equations,using matrix method, ...

    Text Solution

    |

  13. Find values of x if i) |[2 , 4],[ 5, 1]|=|[2 x, 4], [6, x]| ii) ...

    Text Solution

    |

  14. Find the values of x, if |(2,3),(4,5)|=|(x,3),(2x,5)|

    Text Solution

    |

  15. Using properties of determinants prove the following. abs[[1,x,x^2...

    Text Solution

    |

  16. Find the adjoint of B=[[1,-1,2],[2,3,5],[-2,0,1]]

    Text Solution

    |

  17. By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,...

    Text Solution

    |

  18. Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

    Text Solution

    |

  19. If A = [[1,2],[4,2]] then show that |2A|= 4|A|

    Text Solution

    |

  20. Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

    Text Solution

    |