Home
Class 12
MATHS
Using properties of determinants, prove ...

Using properties of determinants, prove that :
`|{:(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1):}|=a^(2)+b^(2)+c^(2)+1`

A

`1+a^(2)+b^(2)+c^(2)`

B

`a^(2)+b^(2)+c^(2)`

C

`(a+b+c)^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise PART-III|18 Videos
  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise PART-IV|1 Videos
  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise PART-II|26 Videos
  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos
  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2

Using properties of determinants, prove the following |(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using properties of determinants, prove the following |(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

Using properties of determinants, prove that 3 2 (a 1) 3 3 1 2a 1 a 2 1 a 2a 2a

Using properties of determinants, prove that: |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))|=(1+a^(2)+b^(2))^(3)

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

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

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

RESONANCE ENGLISH-MATRICES & DETERMINANT-EXERCISE-2
  1. Flind the product of two matrices A =[[cos^(2) theta , cos theta sin...

    Text Solution

    |

  2. If AB=O for the matrices A=[[cos^2theta,costhetasintheta],[costhetasin...

    Text Solution

    |

  3. If X=[(3,-4),(1,-1)] the value of X^(n) is

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. The number of nxxn matrix A and B such that AB - BA = I is. . .

    Text Solution

    |

  6. If B, C are square matrices of order n and if A = B + C, BC = CB,C^2=0...

    Text Solution

    |

  7. How many 3 x 3 skew symmetric matrices can be formed using numbers -2,...

    Text Solution

    |

  8. If A is a skew-symmetric matrix and n is an even natural number,...

    Text Solution

    |

  9. Matrix A such that A^(2)=2A-I, where I is the identity matrix, then fo...

    Text Solution

    |

  10. about to only mathematics

    Text Solution

    |

  11. " If "|{:(sin 0 cos phi,,sin 0 sin phi,,cos 0),(cos 0 cos phi,, cos 0 ...

    Text Solution

    |

  12. Prove that |{:(1+a^(2)+a^(4),,1+ab+a^(2)b^(2),,1+ac+a^(2)c^(2)),(1+ab+...

    Text Solution

    |

  13. Using properties of determinants, prove that : |{:(a^(2)+1,ab,ac),(b...

    Text Solution

    |

  14. Value of the Delta=|{:(,a^(3)-x,a^(4)-x,a^(5)-x),(,a^(5)-x,a^(6)-x,a^(...

    Text Solution

    |

  15. If Delta1=|[2a,b,e],[2d,e,f],[4x,2y,2z]|,Delta2=|[f,2d,e],[2z,4x,2y],[...

    Text Solution

    |

  16. From the matrix equation AB=AC, we conclude B=C provided.

    Text Solution

    |

  17. Let A=|{:(,-2,7,sqrt3),(,0,0,-2),(,0,2,0):}| and A^(4)=lambda,I,"then"...

    Text Solution

    |

  18. If A is 3 xx 3 square matrix whose characteristics polynomical equatio...

    Text Solution

    |

  19. If a,b,c are non-zeros, then the system of equations {:((alpha+a)x+a...

    Text Solution

    |