Home
Class 10
MATHS
For which value (s) of lambda, do the pa...

For which value (s) of `lambda`, do the pair of linear equations `lambdax + y = lambda^(2)` and `x + lambda y = 1 ` have
(i) no solution ? (ii) infinitely many solutions ?
(iii) a unique solution ?

Text Solution

AI Generated Solution

To solve the problem, we need to determine the values of \( \lambda \) for the pair of linear equations: 1. \( \lambda x + y = \lambda^2 \) (Equation 1) 2. \( x + \lambda y = 1 \) (Equation 2) We will analyze the conditions for: (i) No solution (ii) Infinitely many solutions ...
Promotional Banner

Topper's Solved these Questions

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    NCERT EXEMPLAR|Exercise Exercise 3.3 Short Answer Type Questions|2 Videos

  • INTRODUCTION TO TRIGoNOMETRY AND ITS APPLICATIONS

    NCERT EXEMPLAR|Exercise Introduction To Trigonometry And Its Applications|60 Videos

  • POLYNOMIALS

    NCERT EXEMPLAR|Exercise Polynomials|29 Videos

Similar Questions

Explore conceptually related problems

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have no solution?

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have a unique solution?

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have infinitely many solutions?

The value of k, for which the pair of linear equations k x + y = k^(2) and x + k y = 1 has infinitely many solution, is :

The system of linear equations x + lambda y-z =0, lambdax-y -z =0, x + y -lambda z =0 has a non-trivial solution for

The system of linear equations x+lambda y-z=0 , lambda x-y+z=0 , x+y-lambda z=0 has a non-trivial solution for

The value of k, for which the pair of linear equations kx+y=k^(2) and x + ky = 1 has infinitely many solution, is:

Calculate the value of c for which pair of linear equations cx - y = 2 and 6x - 2y = 4 will have infinitely many solutions.

The set of all values of lambda for which the systme of linear equations x-2y-2z = lambda x, x +2y +z = lambda y " and "-x-y = lambdaz has a non-trivial solution.

The set of all values of lambda for which the system of linear equations x - 2y - 2z = lambdax x + 2y + z = lambday -x -y = lambdaz has a non-trivial solution