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Find the value of '\lambda ' for which the set of equations

            x + y - 2z = 0, 2x - 3y + z= 0, x - 5y + 4z = \lambda are consistent.

  • Option 1)

    1

  • Option 2)

    -1

  • Option 3)

    0

  • Option 4)

    2

 

Answers (1)

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As we have learned

Consistent system of linear equation -

If the system of equations has one or more solutions 

-

 

 

A non-homogenous system has unique solution,

                        if D\neq  0 and has infinite solutions if D = D1 = D2 = D3 = 0.

                        Now D = \begin{vmatrix} 1 &1 &-2 \\ 2& -3 & 1\\ 1&-5 &4 \end{vmatrix} = 0. Hence D1,D2& D3 should all be zero \Rightarrow\lambda = 0.


Option 1)

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Option 2)

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Option 3)

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Option 4)

2

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