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The system of linear equation  x+y+z=2,\, \, 2x+y-z=3, \, \, 3x+2y+kz=4

has a unique solution if

  • Option 1)

    K\neq0

  • Option 2)

    -1<K<1

  • Option 3)

    -2<K<2

  • Option 4)

    K= 0

 

Answers (1)

best_answer

As learnt in

Solution of a system of equations -

x_{1},x_{2},\cdot \cdot \cdot ,x_{n} satisfy the system of linear equations  A_{x}=B

- wherein

 

 For unique solution \Delta \neq 0

\begin{vmatrix} 1 & 1 &1 \\ 2 & 1 & -1\\ 3 & 2 & k \end{vmatrix} \neq 0

1(k+2)-1(2k+3)+1(1)\neq 0

k+2-2k-3+1 \neq 0

-k \neq 0\:\:\:\:\:\:\:\:\:\Rightarrow k \neq 0


Option 1)

K\neq0

This option is correct.

Option 2)

-1<K<1

This option is incorrect.

Option 3)

-2<K<2

This option is incorrect.

Option 4)

K= 0

This option is incorrect.

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Plabita

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