Consider the augmented matrix

\[ \left[\begin{array}{ccc|c} 4 & 1 & 7 & 6 \\ -5 & -4 & -6 & -2 \\ -1 & 1 & -3 & -4 \\ -3 & 0 & -6 & -6 \end{array}\right] \]

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

Answer:

  1. \[\begin{matrix} 4 \, x_{1} & + & x_{2} & + & 7 \, x_{3} & = & 6 \\ -5 \, x_{1} & - & 4 \, x_{2} & - & 6 \, x_{3} & = & -2 \\ -x_{1} & + & x_{2} & - & 3 \, x_{3} & = & -4 \\ -3 \, x_{1} & & & - & 6 \, x_{3} & = & -6 \\ \end{matrix}\]

  2. \[ x_{1} \left[\begin{array}{c} 4 \\ -5 \\ -1 \\ -3 \end{array}\right] + x_{2} \left[\begin{array}{c} 1 \\ -4 \\ 1 \\ 0 \end{array}\right] + x_{3} \left[\begin{array}{c} 7 \\ -6 \\ -3 \\ -6 \end{array}\right] = \left[\begin{array}{c} 6 \\ -2 \\ -4 \\ -6 \end{array}\right] \]