Consider the system of equations

\[\begin{matrix} -3 \, x & - & y & + & 7 \, z & = & 1 \\ & & y & - & 5 \, z & = & 6 \\ -x & & & + & 3 \, z & = & 0 \\ -2 \, x & - & y & + & 7 \, z & = & -2 \\ \end{matrix}\]

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

Answer:

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

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