Home
Class 12
MATHS
Prove that the following. [[a,b,c],[x,y,...

Prove that the following. `[[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[z,c,r]]=[[x,y,z],[p,q,r],[a,b,c]]`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise PROBLEM|63 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise PROBLEM|19 Videos

Similar Questions

Explore conceptually related problems

Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2[[a,b,c],[p,q,r],[x,y,z]]

Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c],[p,q,r],[x,y,z]]

Evaluate the following determinants: [[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]]

Simplify: "[x y z]"xx[[a,h,g],[h,b,f],[g,f,c]]xx[[x],[y],[z]]

Write the value of x-y + z from the following equation. [[x+y+z],[x+z],[y+z]]=[[9],[5],[7]] .

Write the value of x-y+z from the relation [[x+y+z],[x+z],[y+z]]=[[4],[8],[5]] .

Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

State the order of the following matrices . [{:(x,y),(y,z),(z,x):}]

Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(z-x)

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

MODERN PUBLICATION-DETERMINANTS-PROBLEM
  1. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

    Text Solution

    |

  2. Solve the following : [[1+x,1,1],[1,1+x,1],[1,1,1+x]]=0

    Text Solution

    |

  3. Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[...

    Text Solution

    |

  4. Prove that the following. [[a+d,a+d+k,a+d+c],[c,c+b,c],[d,d+k,d+c]]=ab...

    Text Solution

    |

  5. Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+...

    Text Solution

    |

  6. Prove that [[b^2c^2, bc,b+c],[c^2a^2,ca,c+a],[a^2b^2,ab,a+b]] = 0

    Text Solution

    |

  7. Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

    Text Solution

    |

  8. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

    Text Solution

    |

  9. Prove that [[1,a,a^2 - bc],[1,b,b^2 - ca],[1,c,c^2 - ab]]

    Text Solution

    |

  10. Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=...

    Text Solution

    |

  11. Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+...

    Text Solution

    |

  12. Factorize the following. [[a,b,c],[b+c,c+a,a+b],[a^2,b^2,c^2]]

    Text Solution

    |

  13. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

    Text Solution

    |

  14. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

    Text Solution

    |

  15. Prove that [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] = 1+a^2+b^2+c...

    Text Solution

    |

  16. Show that [[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]] = 3(a+b+c)(ab...

    Text Solution

    |

  17. Show that the homogenous system of equations x-2y+z = 0 x+y-z = 0 ...

    Text Solution

    |

  18. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

    Text Solution

    |

  19. Examining consistency and solvability, solve the following equation by...

    Text Solution

    |

  20. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

    Text Solution

    |