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I need help with - Matrices and Determinants - JEE Main-3

Consider the system of equation

            x + 2y - z = 6

            2x + 3y + z = 3

            3x + 5y + \lambdaz = \mu then system has     

  • Option 1)

    Infinite solutions, if  \lambda = 0, \mu = 9

  • Option 2)

    No solution, if \lambda \neq 0, \mu = 9

  • Option 3)

    Unique solution, if \lambda \neq 0, \mu \neq  9

  • Option 4)

    All of these 

 
Answers (1)
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As we have learned

Inconsistent system of linear equation -

If the system of equations has no solutions

-

 

If \lambda = 0, then 3rd equation is I + II, so, for infinite solutions \mu = 6 + 3

            Similarly other cases.

 

 


Option 1)

Infinite solutions, if  \lambda = 0, \mu = 9

Option 2)

No solution, if \lambda \neq 0, \mu = 9

Option 3)

Unique solution, if \lambda \neq 0, \mu \neq  9

Option 4)

All of these 

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