Exercise Set 1.1 – No. 7

Find the augmented matrix for the linear system:

\large {\color{blue} (a) \begin{matrix} -2x_1 & = & 6 \\ 3x_1 & = & 8 \\ 9x_1 & = & -3 \end{matrix} }

\large {\color{Blue} \begin{bmatrix} -2 & 6\\ 3 & 8 \\ 9 & -3 \end{bmatrix} }

\large {\color{blue} (b)\; \begin{matrix} 6x_1 & - & x_2 & + & 3x_3 & = & 4 \\ & & 5x_2 & - & x_3 & = & 1 \end{matrix} }

\large {\color{Blue} \begin{bmatrix} 6 & -1 & 3 & 4\\ 0 & 5 & -1 & 1 \end{bmatrix} }

\large {\color {Blue} (c) \begin{matrix} & 2x_2 & & -3x_4 & +x_5 &=0 \\ -3x_1 & -x_2 & +x_3 & & &= -1 \\ 6x_1 & +2x_2 & -x_3 & +2x_4 & -3x_5 &= 6 \end{matrix} }

\large {\color{Blue} \begin{bmatrix} 0 & 2 & 0 & -3 & 1 & 0\\ -3 & -1 & 1 & 0 & 0 & -1\\ 6 & 2 & -1 & 2 & -3 & 6 \end{bmatrix} }