Home
Class 12
MATHS
Prove, using properties of determinants:...

Prove, using properties of determinants: `|y+k y y y y+k y y y y+k|=k^2(3y+k)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(c ) (SHORT ANSWER TYPE QUESTIONS)|4 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(d) (SHORT ANSWER TYPE QUESTIONS)|4 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (I))|19 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

Prove, using properties of determinants: |[y+k, y, y],[ y, y+k, y],[ y, y, y+k]|=k^2(3y+k)

Using properties of determinants , find the value of k if |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|=k(x^(3)+y^(3)) .

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

kx + 3y = 3, 12 x + k y = 6 .

For what value of k system of equations 3x + 4y = 19, y - x = 3 and 2x + 3y = k has a solution ?

3x - y - 5 = 0 , 6x - 2y + k = 0 ( k ne 0 )

Find the value of x, if 2x + 3y + k = 12 and x + 6y + 2k = 18

If k_r is the coefficient of y^(r - 1) in the expansion of (1 + 2y)^10 , in ascending powers of y , determine 'r' when (k_(r + 2))/(k_r) = 4

{:(2x - 3y = k),(4x + 5y = 3):}

26. If (h,k) is orthocentre of triangle formed by lines 3y=2x,3x=2y, and x+y=7 then (h-k) is

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))
  1. By using properties of determinants, prove the following: |x+4 2x2x...

    Text Solution

    |

  2. Prove: |x+4xxxx+4xxxx+4|=16(3x+4)

    Text Solution

    |

  3. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

    Text Solution

    |

  4. for x,x,z gt 0 Prove that |{:(1,,log(x)y,,log(x)z),(log(y)x,,1,,log(y)...

    Text Solution

    |

  5. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

    Text Solution

    |

  6. Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)...

    Text Solution

    |

  7. Prove the following : |{:(1,a,a),(a,1,a),(a,a,1):}|=(2a+1)(1-a)^(2)

    Text Solution

    |

  8. Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}|

    Text Solution

    |

  9. Prove the following : |{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-...

    Text Solution

    |

  10. |[1,a, bc] ,[1, b, ca], [1, c, ab]| =(a-b)(b-c)(c-a)

    Text Solution

    |

  11. Prove the following : |{:(bc,a,1),(ca,b,1),(ab,c,1):}|=(a-b)(b-c)(a-...

    Text Solution

    |

  12. Prove the following : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=|...

    Text Solution

    |

  13. Prove the following : |{:(a^(2),a,b+c),(b^(2),b,c+a),(c^(2),c,a+b):}...

    Text Solution

    |

  14. Prove that |{:(a,b,c),(a^(2),b^(2),c^(2)),(b+c,c+a,a+b):}|=(a-b)(b-c)(...

    Text Solution

    |

  15. Prove the following : |{:(x,x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y):}...

    Text Solution

    |

  16. Prove the following : |{:(alpha,alpha^(2),beta+gamma),(beta,beta^(2)...

    Text Solution

    |

  17. |[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^3+b^3+c^3-3abc

    Text Solution

    |

  18. Evaluate the following: |[a^2+2a, 2a+1, 1],[2a+1, a+2, 1],[3,3,1]|

    Text Solution

    |

  19. Given : a^(2)+b^(2)+c^(2) =0 Prove the following : |{:(b^(2)+c^(2...

    Text Solution

    |

  20. |[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...

    Text Solution

    |