Home
Class 12
MATHS
Show that: |a b-cc+b a+c b c-a a-bb+a c|...

Show that: `|a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot`

Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

    ALLEN|Exercise EX -JA|8 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ALLEN|Exercise All Questions|145 Videos

Similar Questions

Explore conceptually related problems

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))

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)

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: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

3. Using properties of determinants, show that :|[b+c,a,b] , [c+a,c,a] , [a+b,b,c]| = (a + b + c) (a-c)^2

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))

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .

ALLEN-DETERMINANTS-All Questions
  1. Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

    Text Solution

    |

  2. By using properties of determinants. Show that:|1+a^2-b^2 2a b-2b2a b1...

    Text Solution

    |

  3. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

    Text Solution

    |

  4. Absolute value of sum of roots of the equation |x+22x+3 3x+4 2x+3 3x+4...

    Text Solution

    |

  5. a+b+c=0, solve for x : [[a-x,c,b],[c,b-x,a],[b,a,c-x]]=0

    Text Solution

    |

  6. Prove that '[[b-c,c-a,a-b],[b'-c'],[c'-a'][a'-b'],[b"-c",c"-a",a"-b"]]...

    Text Solution

    |

  7. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

    Text Solution

    |

  8. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

    Text Solution

    |

  9. If Dr=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then p...

    Text Solution

    |

  10. If D=|[1/z,1/z,-(x+y)/(z^2)],[-(y+z)/(x^2),1/x,1/x],[-(y(y+z)/(x^2z))...

    Text Solution

    |

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

    Text Solution

    |

  12. Solve the following sets of equations using Cramer's rule and remark a...

    Text Solution

    |

  13. Solve the following sets of equation using Cramers rule and remark ...

    Text Solution

    |

  14. Solve the following sets of equation using Cramers rule and remark ...

    Text Solution

    |

  15. . For what values of lambda and mu the system of equations x+y+z=6, x+...

    Text Solution

    |

  16. Find those values of c for which the equations: 2x+3y=3,(c+ 2)x + (c +...

    Text Solution

    |

  17. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

    Text Solution

    |

  18. If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2...

    Text Solution

    |

  19. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

    Text Solution

    |

  20. Solve the system of equations : z+ay+a^2x+a^3=0 z+by+b^2x+b^3=0 z+cy+c...

    Text Solution

    |