Consider the vector equation.

\[ x_{1} \left[\begin{array}{c} 0 \\ -1 \\ -1 \\ -4 \end{array}\right] + x_{2} \left[\begin{array}{c} -4 \\ 2 \\ -3 \\ 8 \end{array}\right] + x_{3} \left[\begin{array}{c} 4 \\ -2 \\ 3 \\ -8 \end{array}\right] = \left[\begin{array}{c} 8 \\ -2 \\ 8 \\ -8 \end{array}\right] \]

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

Answer:

  1. \[\begin{matrix} & & 4 \, x_{2} & + & 4 \, x_{3} & = & 8 \\ -x_{1} & + & 2 \, x_{2} & - & 2 \, x_{3} & = & -2 \\ -x_{1} & - & 3 \, x_{2} & + & 3 \, x_{3} & = & 8 \\ -4 \, x_{1} & + & 8 \, x_{2} & - & 8 \, x_{3} & = & -8 \\ \end{matrix}\]

  2. \[ \left[\begin{array}{ccc|c} 0 & -4 & 4 & 8 \\ -1 & 2 & -2 & -2 \\ -1 & -3 & 3 & 8 \\ -4 & 8 & -8 & -8 \end{array}\right] \]