Home
Class 12
MATHS
The system of homogenous equations tx+...

The system of homogenous equations
`tx+(t+1)y+(t-1)z=0`, `(t+1)x+ty+(t+2)z=0`, `(t-1)x+(t+2)y+tz=0` has a non trivial solution for

A

exactly three real values of `t`

B

exactly two real values of `t`

C

exactly one real values of `t`

D

infinite number of values of `t`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` To have a non-trivial solution
`|{:(t,t+1,t-1),(t+1,t,t+2),(t-1,t+2,t):}|=0`
`implies2t+1=0impliest=-(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise JEE ADVANCED|38 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

Similar Questions

Explore conceptually related problems

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

The value of k for which the system of equations x+ky-3z=0 , 3x+ky-2z=0, 2x+3y-4z=0 has a non -trivial solution is

Find the equation to the locus represented by x=(2+t+1)/(3t-2), y=(t-1)/(t+1) wher t is variable parameter.

The eccentricity of the hyperbola 2x = a(t + (1)/(t)), 2y = a(t-(1)/(t))

If y(t) is the solution of the differential equation (t+1)(dy)/(dt)-ty=1 and y(0)=-1 , then the value of y at t=1 is -

Find the real values of lambda for which the following system of linear equations has non -trivial solutions: x+y-3z=0,( 1+lambda)x+(2+lambda)y-8z=0 , x-(1+lambda)y+(2+lambda)z=0 .

Solve the equation for x, y, z and t, if 2[(x, y),(z,t)]+3[(1,-1),(0,2)]=3[(3,5),(4,6)]

The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^2+t+1; t in R , is

Find the equation of tangent to y=int_(x^2)^(x^3)(dt)/(sqrt(1+t^2))a tx=1.

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

CENGAGE PUBLICATION-DETERMINANT-Single correct Answer
  1. |[1/c,1/c,-(a+b)/c^2],[-(b+c)/a^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/...

    Text Solution

    |

  2. The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)...

    Text Solution

    |

  3. Let Delta(1)=|{:(ap^(2),2ap,1),(aq^(2),2aq,1),(ar^(2),2ar,1):}| and De...

    Text Solution

    |

  4. Area of triangle whose vertices are (a,a^2),(b,b^2),(c,c^2) is 1/2 . a...

    Text Solution

    |

  5. Prove that |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaalph...

    Text Solution

    |

  6. If |{:(a,b,1),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,...

    Text Solution

    |

  7. Let |(a,l,m),(l,b,n),(m,n,c)||(bc-n^2,mn-lc,ln-bm),(mn-lc,ac-m^2,ml-an...

    Text Solution

    |

  8. The value of |{:(x^(2)+y^(2),ax+by,x+y),(ax+by,a^(2)+b^(2),a+b),(x+y,a...

    Text Solution

    |

  9. If u=ax+by+cz, v=ay+bz+cx, w=az+bx+cy, then the value of |{:(a,b,c),(b...

    Text Solution

    |

  10. If the number of positive integral solutions of u+v+w=n be denoted by ...

    Text Solution

    |

  11. If f(x), h(x) are polynomials of degree 4 and |(f(x), g(x),h(x)),(a, b...

    Text Solution

    |

  12. If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+...

    Text Solution

    |

  13. If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}|, then lim(xto0...

    Text Solution

    |

  14. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |

  15. Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lamb...

    Text Solution

    |

  16. The system of homogenous equations tx+(t+1)y+(t-1)z=0, (t+1)x+ty+(t+...

    Text Solution

    |

  17. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

    Text Solution

    |

  18. The values of theta, lambda for which the following equations sintheta...

    Text Solution

    |

  19. If the system of equation {:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):} ...

    Text Solution

    |

  20. If A,B,C are the angles of a triangle, the system of equations (sinA...

    Text Solution

    |