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  • The number of real value of alpha for which the system of equations : x+3y+5z=(alpha)x 5x+y+3z=(alpha) y 3x+5y+z=(alpha)z has infinitely many solution is

The number of real value of alpha for which the system of equations : x+3y+5z=(alpha)x 5x+y+3z=(alpha) y 3x+5y+z=(alpha)z has infinitely many solution is

Answers (1)

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Solution:    The equation are

                 (1-alpha )x+3y+5z=0

                 5x+(1-alpha)y+3z=0

                3x+5y+(1-alpha)z=0

 This Homogeneneous system of equations has an infinite

number of solutions if

              Rightarrow          eginvmatrix (1-alpha) & 3 & 5 \5 &(1-alpha) &3 \3 &5 &(1-alpha) endvmatrix=0

  Simplifying , we have

            Rightarrow         (alpha-9)(alpha ^2+6alpha +12)=0

   There is only one  real value of alpha =9 for which this 

   system has infinitely many solution.     

Posted by

Deependra Verma

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