Home
Class 12
MATHS
Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+...

Consider `abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]`

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

Prove that |[a, a+b, a+b+c],[ 2 a, 3 a+2 b, 4 a+3 b+2 c],[ 3 a, 6 a+3 b, 10 a+6 b+3 c]|=a^3

Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] show that abs[A]=-(a^3+b^3+c^3-3abc)

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]|= |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

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

Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] Using the column operation C_1rarrC_1+C_2+C_3 , show that abs[A]=(a+b+c)abs[[1,b,c],[1,c,a],[1,a,b]]

Using properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

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

Which of the following has value not equal to zero ? a) |(8,2,7),(12,3,5),(16,4,3)| b) |(1//a,a^(2),bc),(1//b,b^(2),ac),(1//c,c^(2),ab)| c) |(a+b,2a+b,3a+b),(2a+b,3a+b,4a+b),(4a+b,5a+b,6a+b)| d) |(2,43,6),(7,35,4),(3,17,2)|

Consider the matrices A=[[1,-2],[-1,3]] and B=[[a,b],[c,d]] If AB=[[2,9],[5,6]] , find the values of a,b,c,d

BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2...

    Text Solution

    |

  2. Choose the correct answer from the bracket.The value of the determin...

    Text Solution

    |

  3. Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]

    Text Solution

    |

  4. Choose the correct answer from the bracket.Consider a sqare matrix o...

    Text Solution

    |

  5. Verify A(adjA)=(adjA)A=abs[A]I for the matrix A=[[5,-2],[3,-2]]that,...

    Text Solution

    |

  6. Choose the correct answer from the bracket. If A=[(cosx,sinx),(-sinx,c...

    Text Solution

    |

  7. Find the inverse of the following A=[[1,-1,2],[0,2,-3],[3,-2,4]]

    Text Solution

    |

  8. If A=[[2,3],[1,-2]] and A^-1=kA,then the value of 'k' is

    Text Solution

    |

  9. If A=[[1,-1,1],[2,-1,0],[1,0,0]], Find A^2

    Text Solution

    |

  10. If A=[[1,-1,1],[2,-1,0],[1,0,0]], Show that A^2=A^-1

    Text Solution

    |

  11. Choose the correct answer. If each element of a third order square mat...

    Text Solution

    |

  12. Consider the matrix A=[(-8,5),(2,4)] Show that 'A' satisfies the equat...

    Text Solution

    |

  13. Consider the matrix A=[(-8,5),(2,4)] Hence find A^-1.

    Text Solution

    |

  14. If A and B are matrices of order 3 such that abs[A]=-1,abs[B]=3,then...

    Text Solution

    |

  15. If A=[(1,tanx),(-tanx,1)], Show that, A^TA^-1=[(cos2x,-sin2x),(sin2x,c...

    Text Solution

    |

  16. If A=[[1,1,5],[0,1,3],[0,-1,-2]] what is the value of abs[3A]?

    Text Solution

    |

  17. Find the equation of the line joining the points(1,2) and (-3,-2) us...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |