Home
Class 12
MATHS
The value of the det. |[x+y,y+z,z+x],[z,...

The value of the `det. |[x+y,y+z,z+x],[z,x,y],[1,1,1]|` is

Text Solution

Verified by Experts

The correct Answer is:
`0`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-III (True or False questions)|25 Videos
  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise (Question carrying 2 marks)|21 Videos
  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-I (Multiple choice questions)|47 Videos
  • DEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTION CARRYING 4 MARKS|8 Videos
  • DIFFERENTAL QUATIONS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|41 Videos

Similar Questions

Explore conceptually related problems

The value of |[[1,x,y+z],[1,y,z+x],[1,z,x+y]]| is

Write the value of Delta = |(x+y, y +z , z +x),(z, x,y),(-3,-3,-3)|

Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y),(1,1,1)|

Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x , y),(1,1,1):} = 0

Find the values of x, y, z if the matrix A = [[0,2y,z],[x,y,-z],[x,-y,z]] satisfy the equation A'A = I

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

Prove that : |[x+y+z,-z,-y],[-z, x+y+z, -x],[-y,-x,x+y+z]|= 2(x+y)(y+z)(z+x)

Show that: |[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]|=(x+y+z)^3

ACCURATE PUBLICATION-DETERMINANTS-Type-II (Fill in the blanks questions)
  1. If A= diag (5, 2, l) then det A is equal to :

    Text Solution

    |

  2. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

    Text Solution

    |

  3. The value of the det. |[x+y,y+z,z+x],[z,x,y],[1,1,1]| is

    Text Solution

    |

  4. The value of |{:(1,p,q+r),(1,q,r+p),(1,r,p+q):}| is……

    Text Solution

    |

  5. If area of a triangle is 4 sq. units with vertices (k,0), (4,0) and (0...

    Text Solution

    |

  6. A is a square matrix of order 3 and |A|=7, then the value of |adjA| is...

    Text Solution

    |

  7. If A is non-singular matrix of order 3 and |A|=7 then |adjA| equals………...

    Text Solution

    |

  8. If |A|=2, where A is a 2xx2 matrix, then |adjA| is …………

    Text Solution

    |

  9. If A=[{:(3,2),(1,7):}], then A(adjA) equals……..

    Text Solution

    |

  10. If A=[{:(3,2),(1,9):}], then A(adjA) equals……..

    Text Solution

    |

  11. Select the Correct Option If A is an invertible matrix of order 2, the...

    Text Solution

    |

  12. If x. y, z are non- real number", then the inverse of matrix A = [[x,0...

    Text Solution

    |

  13. If A,B,C are the angles of a triangle, then Delta=|{:(sin^(2)A, cotA...

    Text Solution

    |

  14. The determinant Delta=|{:(sqrt(23)+sqrt(3),sqrt(5),sqrt(5)),(sqrt(15)+...

    Text Solution

    |

  15. The value of the determinant Delta=|{:(sin^(2)23^(@)sin^(2)67^(@)cos18...

    Text Solution

    |

  16. If A is matrix of order 3xx3, then |3A|=……….

    Text Solution

    |

  17. If A is invertible matrix of order 3xx3, then |A^(-1)|……….

    Text Solution

    |

  18. If x,y,z epsilon R, then the value of determinant |{:((2^(x)+2^(-x))^(...

    Text Solution

    |

  19. If cos2theta=0, then |{:(0,costheta,sintheta),(costheta,sintheta,0),(s...

    Text Solution

    |

  20. If A is matrix of order 3xx3, then (A^(2))^(-1)=…….

    Text Solution

    |