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

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTION -II)|3 Videos

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC-2 SOLUTIONS OF SYSTEM OF LINEAR EQUATIONS (LONG ANSWER TYPE QUESTIONS -II )|24 Videos

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (SHORT ANSWER TYPE QUESTIONS-II)|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OSWAAL PUBLICATION|Exercise MVT AND ROLLE.S THEOREM ( SHORT ANSWER TYPE QUESTIONS-II)|5 Videos

  • DIFFERENTIAL EQUATIONS

    OSWAAL PUBLICATION|Exercise HOMOGENEOUS DIFFERENTIAL EQUATIONS (Long Answer Type Questions - III)|8 Videos

Similar Questions

Explore conceptually related problems

|(y +k, y , y),(y, y + k, y),(y, y, y+k)|= k^(2)(3y + k) .

Give the relation between Y,K and eta

Find the area of the triangle formed by the lines y - x = 0, x + y = 0 " and " x - k = 0 .

If the sum of all value of x satisfying the system of equations tan x + tan y+ tan x* tan y=5 sin (x +y)=4 cos x * cos y is (k pi )/2 , where x in (0, (pi)/(2)) then find the values of k .

Give the relation between Y, K and sigma.

If the system of equation : x + y + z = 0 , 2 x + 3y + 4z = 0 , kx + y - z = 0 has a non - zero solution , then the value of k is

Prove that |(x,y,y),(y,x,y),(y,y,x)| = (x + 2y)(x - y)^(2)

If the midpoint of the line joining (3,4) and (K, 7) is ( y) and 2x + 2y + 1= 0, find K.

the number of value of k , for which the system of equations : (k+1)x+8y=4k kx+(k+3)y=3k-1 has no solution is :

The number of values of k for which the system of equations : (k+1)x+8y=4k kx+(k+3)y=3k-1 has no solution is:

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...

    Text Solution

    |

  2. Find the equation of the line joining A( 1,3) and B (0,0) using det...

    Text Solution

    |

  3. Using properties of determinants, prove the following: |xx+y x+2y\...

    Text Solution

    |

  4. Using properties of determinants, prove the following: |alphabetag...

    Text Solution

    |

  5. 15. Using properties of determinants, prove the following |[a,b,c],[a-...

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(...

    Text Solution

    |

  8. 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

    |

  9. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

    Text Solution

    |

  10. Using the Properties of determinants, prove that following: {:|(-a^2...

    Text Solution

    |

  11. Using the Properties of determinants, prove the following: {:|(1,1...

    Text Solution

    |

  12. If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 and x, y, z are ...

    Text Solution

    |

  13. Using properties of determinants, solve the following for x: |x-2 ...

    Text Solution

    |

  14. Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...

    Text Solution

    |

  15. Using Properties of determinants, solve the following for x: {:|(x+a...

    Text Solution

    |

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

    Text Solution

    |

  17. Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...

    Text Solution

    |

  18. Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^2

    Text Solution

    |

  19. |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

    Text Solution

    |

  20. Prove, using Properites of determinants, {:|(a+bx^2,c+dx^2,p+qx^2),(...

    Text Solution

    |