Question-5

Consider the following system of equations:

\[ \begin{aligned} 0x_{1}+x_{2}+0x_{3}+0x_{4} & =1\\ 0x_{1}+0x_{2}+x_{3}+0x_{4} & =1 \end{aligned} \]

Comment on the dependent and independent variables for the above system.

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We can form the matrix corresponding to this system:

\[ \begin{bmatrix}0 & \boldsymbol{1} & 0 & 0\\ 0 & 0 & \boldsymbol{1} & 0 \end{bmatrix} \]

The second and third columns are pivot columns. Hence \(x_{2}\) and \(x_{3}\) are dependent variables. \(x_{1}\) and \(x_{4}\) are independent variables.