Question-4

Express the following system in matrix-vector form and solve it:

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

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We have:

\[ A=\begin{bmatrix}0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0\\ 1 & 1 & 0 & 0\\ 0 & 0 & 1 & 1 \end{bmatrix},\,\,\,\,x=\begin{bmatrix}x_{1}\\ x_{2}\\ x_{3}\\ x_{4} \end{bmatrix},\,\,\,\,b=\begin{bmatrix}1\\ 1\\ 1\\ 1 \end{bmatrix} \]

We note that the second row is a zero row in \(A\), but the corresponding component in the vector \(b\) is non-zero. Hence, this system doesn’t have any solution.