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

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) `

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

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)

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)

Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,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

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)

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)) ]:}

Show that |{:(a^2 + x^2 , ab, ac),(ab, b^2 + x^2 , bc),(ac, bc, c^2 +x^2):}| is divisible by x^4

Using the property of determinants and without expanding {:[( 1,bc,a(a+c) ),(1,ca,b( c+a)) ,( 1,ab,c(a+b) )]:}=0

Show that |(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2))| is divisible by x^(2) .

Prove that |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))|=4a^(2)b^(2)c^(2).

CENGAGE-DETERMINANTS-All Questions
  1. If |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c) xx(x + a + b...

    Text Solution

    |

  2. If a(1), a(2), a(3), ………, a(n)….. are in G.P., then the determinant De...

    Text Solution

    |

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

    Text Solution

    |

  4. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually per...

    Text Solution

    |

  5. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

    Text Solution

    |

  6. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

    Text Solution

    |

  7. If lines p x+q y+r=0,q x+r y+p=0a n dr x+p y+q=0 are concurrent, th...

    Text Solution

    |

  8. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

    Text Solution

    |

  9. Find the value of lambda if 2x^2+7x y+3y^2+8x+14 t+lambda=0 represents...

    Text Solution

    |

  10. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, ...

    Text Solution

    |

  11. If A , B ,C are angles of a triangles, then the value of |[e^(2i A),...

    Text Solution

    |

  12. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...

    Text Solution

    |

  13. Let "Delta"r=|r-1n6(r-1)^2 2n^2 4n-2(r-1)^2 3n^3 3n^2-3n|dot Show that...

    Text Solution

    |

  14. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

    Text Solution

    |

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

    Text Solution

    |

  16. Find the area of a triangle having vertices A(3,2),B(11 ,8), and C(8,1...

    Text Solution

    |

  17. If Dk=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum(k=1)^n Dk=56. then n eq...

    Text Solution

    |

  18. If a!=p ,b!=q ,c!=ra n d|p b c a q c a b r|=0, then find the value of ...

    Text Solution

    |

  19. If x1,x2,x3 as well as y1, y2, y3 are in G.P. with same common rati...

    Text Solution

    |

  20. If the linesa1x+b1y+1=0,\ a2x+b2y+1=0\ a n d\ a3x+b3y+1=0 are concurre...

    Text Solution

    |