Home
Class 11
MATHS
Prove that|(a,b),(c,d)|^(2)=|(a^(2)+c^(2...

Prove that`|(a,b),(c,d)|^(2)=|(a^(2)+c^(2),ab+cd),(ab+cd,b^(2)+d^(2))|`

Text Solution

Verified by Experts

The correct Answer is:
`=|(a^(2)+c^(2),ab+cd),(ab+cd,b^(2)+d^(2))|`
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 7.1|33 Videos

  • MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 7.2|21 Videos

  • INTRODUCTION TO PROBABILITY THEORY

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Choose the correct option for the following)|39 Videos

  • SETS,RELATIONS AND FUNCATIONS

    PREMIERS PUBLISHERS|Exercise II. Choose the correct option for the following. (M.C.Q)|35 Videos

Similar Questions

Explore conceptually related problems

Prove that |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))|=4a^(2)b^(2)c^(2).

Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) ]:} =4a^(2) b^(2) c^(2)

Show that |(b+c,bc,b^(2)c^(2)),(c+a,ca,c^(2)a^(2)),(a+b,ab,a^(2)b^(2))|=0 .

Show that |(0,a,c),(a,0,b),(c,b,0)|^(2)=|(2ac,ab,bc),(ab,-a^(2),-ac+b^(2)),(bc,-ac+b^(2),-c^(2))|

Show that |{:(b+c,bc,b^(2)c^(2)),(c+a,ca,c^(2)a^(2)),(a+b,ab,a^(2)b^(2)):}| = 0

Prove that matrix [((b^(2)-a^(2))/(a^(2)+b^(2)),(-2ab)/(a^(2)+b^(2))),((-2ab)/(a^(2)+b^(2)),(a^(2)-b^(2))/(a^(2)+b^(2)))] is orthogonal.

If a,b and c are non- zero real number then prove that |{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|

Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^(2)),(ab-c^(2),,bc-a^(2),,ca-b^(2)):}| |{:(a^(2),,c^(2),,2ca-b^(2)),(2ab-c^(2),,b^(2),,a^(2)),(b^(2),,2ac-a^(2),,c^(2)):}|.

PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-PROBLEMS FOR PRACTICE .(II CHOOSE THE CORRECT OPTION FROM THE FOLLOWING)
  1. Prove that|(a,b),(c,d)|^(2)=|(a^(2)+c^(2),ab+cd),(ab+cd,b^(2)+d^(2))|

    Text Solution

    |

  2. If a(ij)=i^(2)-j and A=(a(ij))(2xx2)is:

    Text Solution

    |

  3. Solve|(x-1,2),(3,x-2)|=0

    Text Solution

    |

  4. If 2x+[(3,1),(5,-3)]=[(-1,5),(3,-1)]then x is

    Text Solution

    |

  5. If A=[(3,2,1),(0,4,2),(1,2,3)]and B=[(3,2,0),(4,8,0),(-1,6,2)],then

    Text Solution

    |

  6. If the points (2,-4)(6,2)(4,x) are collinear than x is:

    Text Solution

    |

  7. If the square matrix |(alpha,Beta),(Beta,-alpha)|is a unit matrix of o...

    Text Solution

    |

  8. A=[(0,-2,1),(2,0,-4),(-1,0,0)]then A is

    Text Solution

    |

  9. If A=[(2x,2y,2z),(2a,2b,2c),(2p,2q,2r)]and Delta =[(x,y,z),(a,b,c),(p,...

    Text Solution

    |

  10. If A+2I=[(6,2),(3,-4)],then A(A+I)=

    Text Solution

    |

  11. Find the matrix A if[(1,2),(0,1)]A=[(6,1),(2,1)]

    Text Solution

    |

  12. Find the value of x for which A=[(e^(2x+1),e^(x-2)),(e^(2-x),e^(x-7))]...

    Text Solution

    |

  13. If A is (a(ij))(mxxn),B=(b(ij)(nxxp)),C=(c(ij)(pxxq))Then (ABC)^(T) wi...

    Text Solution

    |

  14. Ifr A is a skew symmetrix matrix of order 3 and B is column matrix of ...

    Text Solution

    |

  15. If A=[(2,4,-5),(3,1,-2),(0,2,-3)],find the coefficient of order 3:

    Text Solution

    |

  16. If A and B are square matrix of same order then (A-B)^(T) is:

    Text Solution

    |

  17. |((x+1/x)^(2),(x-1/x)^(2),1),((y+1/y)^(2),(y-1/y)^(2),1),((z+1/z)^(2),...

    Text Solution

    |

  18. Evaluate |(45,71,26),(35,-21,14),(77,50,40)|:

    Text Solution

    |

  19. if|(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b)|=k(abc).Then k is:

    Text Solution

    |

  20. The area ofDelta with vertices (-2,-3),(3,2),and (-1,x).Then x is:

    Text Solution

    |

  21. Which of the followinf is not true about the matrix[(5,0,0),(0,0,0),(0...

    Text Solution

    |