Home
Class 12
MATHS
Prove that: |(a,a+c,a-b),(b-c,b,b+a),(c+...

Prove that: `|(a,a+c,a-b),(b-c,b,b+a),(c+b,c-a,c)|=(a+b+c)(a^(2)+b^(2)+c^(2))`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    CBSE COMPLEMENTARY MATERIAL|Exercise FOUR MARK QUESTIONS|41 Videos

  • LINEAR PROGRAMMING

    CBSE COMPLEMENTARY MATERIAL|Exercise ONE MARKS QUESTIONS|8 Videos

  • PRACTICE PAPER I

    CBSE COMPLEMENTARY MATERIAL|Exercise Section D|6 Videos

Similar Questions

Explore conceptually related problems

Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)+c^(2)) .

Prove that: |(a,b-c,c-b),(a-c,b,c-a),(a-b,b-a,c)|=(a+b-c)(b+c-a)(c+a-b)

Prove that |(a+b,a,b),(c+a,c,a),(a+b,b,c)|=(a+b+c)(a-c)^2

Prove: |(a, b-c,c-b),( a-c, b, c-a),( a-b,b-a, c)|=(a+b-c)(b+c-a)(c+a-b)

Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

Prove that : |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^(3)

Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)|

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

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

det[[ Show that a,b-c,c+ba+c,b,c-aa-b,b+a,c]]=(a+b+c)(a^(2)+b^(2)+c^(2))

CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-SIX MARK QUESTIONS
  1. Prove that |y z-x^2z x-y^2x y-z^2z x-y^2x y-z^2y z-x^2x y-z^2y z-x^2z ...

    Text Solution

    |

  2. Using elementary tansformations, find the inverse of the matrix A=[(...

    Text Solution

    |

  3. Using matrix method, solve the system of linear equations x-2y=10,2x...

    Text Solution

    |

  4. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

    Text Solution

    |

  5. Find the matrix x for which [(3,2),(7,5)]x[(-1,1),(-2,1)]=[(2,-1),(0,4...

    Text Solution

    |

  6. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

    Text Solution

    |

  7. If a+b+c=0and|(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0, then show that either ...

    Text Solution

    |

  8. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

    Text Solution

    |

  9. |((x-2)^2,(x-1)^2,x^2),((x-1)^2,x^2,(x+1)^2),(x^2,(x+1)^2,(x+2)^2)|=-8...

    Text Solution

    |

  10. Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...

    Text Solution

    |

  11. Prove that: |(a,a+c,a-b),(b-c,b,b+a),(c+b,c-a,c)|=(a+b+c)(a^(2)+b^(2)+...

    Text Solution

    |

  12. If a,b,c are positive and ar the p^(th),q^(th),r^(th) terms respective...

    Text Solution

    |

  13. Prove that (x-2)(x-1) is factor of |(1,1,x),(beta+1,beta+1,beta+x),(3,...

    Text Solution

    |

  14. Show that | (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a...

    Text Solution

    |

  15. Determination the product [{:(,-4,4,4),(,-7,1,3),(,5,-3,-1):}] [{:(,1,...

    Text Solution

    |

  16. If A=[1-1 1 2 1-3 1 1 1], find A^(-1) and hence solve the system of li...

    Text Solution

    |

  17. Solve given system of equations by matrix method: (2)/(a)+(3)/(b)+(4...

    Text Solution

    |

  18. To raise money for an orphanage, students of three schools A, B and C ...

    Text Solution

    |

  19. Two cricket teams honored their players for three values, excellent ba...

    Text Solution

    |

  20. If [(1,2,0),(-2,-1,-2),(0,-1,1)], find A^-1. Using A^-1, solve the sys...

    Text Solution

    |