Consider the system of equations

\[\begin{matrix} x & + & 2 \, y & + & z & = & 5 \\ -2 \, x & - & 3 \, y & - & z & = & -5 \\ x & + & y & + & z & = & 4 \\ 2 \, x & + & 4 \, y & & & = & 2 \\ \end{matrix}\]

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

Answer:

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

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