Home
Class 12
MATHS
Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p...

Show that `|1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.`

Text Solution

Verified by Experts

`L.H.S.=|{:(1,1+p,1+p+q),(2,3+p,4+3p+2q),(3,6+3p,10+6p+3q):}|=|{:(1,1+p,1+p+q),(0,1,2+p),(0,3,7+3p):}|`
`(R_(2)toR_(2)-3R_(1),R_(3)toR_(3)-3R_(1))`
`=1|{:(1,2+p),(3,7+3p):}|=(7+3p)-3(2+p)`
=1=R.H.S.
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4.6|16 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

Similar Questions

Explore conceptually related problems

Show that: |11+p1+p+q23+2p1+3p+2q36+3p1+6p+3q|=1

Show that det[[1,1+p,1+p+q2,3+2p,1+3p+2q3,6+3p,1+6p+3q]]=

Using properties of determinants,prove the det[[1+p,1+p+q2,3+2p,1+3p+2q3,6+3p,1+6p+3q]]=1

Using properties of determinants.Prove that det[[2,3+2p,1+3p+2q3,6+3p,10+6p+3q]]=1

For any natural number p and q (i) p # q = p 3 + q 3 + 3 and p ∗ q = p 2 + q 2 + 2 and p $ q = | p − q | (ii) Max (p,q) = Maximum of (p,q) and Min (p and q) = Minimum of (p,q)The value of [(1 $ 2) # (3$ 4)]*[(5 $ 6) # (7 $ 8)] is :

If the lines p_1x+q_1y=1,p_2x+q_2y=1a n dp_3x+q_3y=1, be concurrent, show that the point (p_1, q_1),(p_2, q_2)a n d(p_3, q_3) are collinear.

If the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

If 2x+1=15;3y-2=16 if x=p(mod 5),y=q(mod 5) then the value of p, q are (i) p=2,q=3 (ii) p=2,q=1 (iii) p=3,q=2 (iv) p=4,q=1

NAGEEN PRAKASHAN-DETERMINANTS-Miscellaneous Exercise
  1. Prove that the determinant [xsinthetacostheta-sintheta-x1costheta1x]is...

    Text Solution

    |

  2. Show without expanding at any stage that: [a,a^2,bc],[b,b^2,ca],[c,c^...

    Text Solution

    |

  3. Evaluate abs[{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta...

    Text Solution

    |

  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

    Text Solution

    |

  5. Solve the equation: |[x+a, b,c],[a,x+b,c],[a,b,x+c]|=0

    Text Solution

    |

  6. Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^...

    Text Solution

    |

  7. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

    Text Solution

    |

  8. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}]. Verify that ltbtgt (i) [adjA]^...

    Text Solution

    |

  9. Evaluate: [[x,y,x+y],[y,x+y,x],[x+y,x,y]]

    Text Solution

    |

  10. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

    Text Solution

    |

  11. Using peoperties of determinants in questions 11 to 15, prove that : ...

    Text Solution

    |

  12. Prove that [[x, x^2 , 1+px^3], [y, y^2, 1+py^3] ,[z, z^2, 1+pz^3]] = (...

    Text Solution

    |

  13. Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

    Text Solution

    |

  14. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

    Text Solution

    |

  15. Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, ...

    Text Solution

    |

  16. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

    Text Solution

    |

  17. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

    Text Solution

    |

  18. Choose the correct answer in questions 17 to 19: If x, y, z are non...

    Text Solution

    |

  19. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

    Text Solution

    |