Home
Class 12
MATHS
By using properties of determinants , s...

By using properties of determinants , show 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) `

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

By using properties of determinants , show that : {:[( a^(2) + 1, ab,ac),(ab,b^(2) + 1,bc),( ca, cb, c^(2) +1) ]:}= 1+a^(2) +b^(2) +c^(2)

By using properties of determinants , show that : (i) {:[( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))]:}=(a-b)(b-c) (c-a) (ii) {:[( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))]:} =( a-b) (b-c)( c-a) (a+b+c)

Using the property of determinants and without expanding {:[( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) ]:} =4a^(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

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

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.

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 |((a+b)^(2),(a-b)^(2),ab),((b+c)^(2),(b-c)^(2),bc),((c+a)^(2),(c-a)^(2),ca)|

Solve: (a - b )x + (a + b)y = a^(2) - 2ab - b^(2) and (a + b) (x + y) = a^(2) + b^(2)

CENGAGE-DETERMINANTS-All Questions
  1. {:[( 1,1+p,1+p+q),( 2,3+2p,4+3p+2q),( 3,6+3p,10+6p+3q)]:}=1

    Text Solution

    |

  2. If |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0, prove that...

    Text Solution

    |

  3. By using properties of determinants , show that : {:[( 1+a^(2) -b^(2...

    Text Solution

    |

  4. Which of the following values of alpha satisfy the equation |{:((...

    Text Solution

    |

  5. solve {:[( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) ]:} = 3( a+...

    Text Solution

    |

  6. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

    Text Solution

    |

  7. \begin{bmatrix}6i&-3i&1\\ 4 &3i& -1\\ ...

    Text Solution

    |

  8. The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]|,w h e r ex ,y ,z are...

    Text Solution

    |

  9. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

    Text Solution

    |

  10. Prove that the value of each the following determinants is zero: |si...

    Text Solution

    |

  11. The number of values of k for which the lines (k+1)x+8y=4k a n dk x+(k...

    Text Solution

    |

  12. Prove that |b+c a-b a c+a b-c b a+b c-a c|=3a b-a^3-b^3-c^3dot

    Text Solution

    |

  13. If |a^2b^2c^2(a+1)^2(b+1)^2(c+1)^2(a-1)^2(b-1)^2(c-1)^2|=k(a-b)(b-c)(c...

    Text Solution

    |

  14. Statement 1: "Delta"=|m y+n z m q+n r m b+n c k z-m x k r-m p k c-m a-...

    Text Solution

    |

  15. Prove that =|1 1 1 a b c b c+...

    Text Solution

    |

  16. If the determinant ∣ cos(θ+ϕ) sinθ −cosθ ​−sin(θ+ϕ) cosθ sinθ cos2ϕ ...

    Text Solution

    |

  17. The system of equations -2x+y+z=a, x-2y+z=b, x+y-2z=c, has: (a)...

    Text Solution

    |

  18. Show that if x1, x2, x3!=0 |x1+a1b1a1b2a1b3a2b1x2+a2b2a2b3a3b1a3b2x3+...

    Text Solution

    |

  19. determinant |"cos theta sin theta -sin theta cos theta

    Text Solution

    |

  20. If Deltar =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1,...

    Text Solution

    |