Consider the augmented matrix

\[ \left[\begin{array}{cccc|c} 1 & -2 & -1 & 3 & 4 \\ 2 & -3 & -3 & 5 & 6 \\ 0 & -3 & 3 & 3 & 6 \end{array}\right] \]

  1. Write a system of scalar equations corresponding to this augmented matrix.
  2. Write a vector equation corresponding to this augmented matrix.

Answer:

  1. \[\begin{matrix} x_{1} & - & 2 \, x_{2} & - & x_{3} & + & 3 \, x_{4} & = & 4 \\ 2 \, x_{1} & - & 3 \, x_{2} & - & 3 \, x_{3} & + & 5 \, x_{4} & = & 6 \\ & & 3 \, x_{2} & + & 3 \, x_{3} & + & 3 \, x_{4} & = & 6 \\ \end{matrix}\]

  2. \[ x_{1} \left[\begin{array}{c} 1 \\ 2 \\ 0 \end{array}\right] + x_{2} \left[\begin{array}{c} -2 \\ -3 \\ -3 \end{array}\right] + x_{3} \left[\begin{array}{c} -1 \\ -3 \\ 3 \end{array}\right] + x_{4} \left[\begin{array}{c} 3 \\ 5 \\ 3 \end{array}\right] = \left[\begin{array}{c} 4 \\ 6 \\ 6 \end{array}\right] \]