Solving a System by Row Reduction: One, None or Infinitely Many Solutions Worksheet with Answer Key

What's on the worksheet

1. Each matrix is the result of row reducing the augmented matrix of a system.
2. Solve the system in x, y, z, w whose augmented matrix is \left[\begin{array}{cccc|c} 1 & -2 & 0 & -4 & 7 \\ -3 & 7 & 2 & 11 & -22 \\ -2 & 1 & -5 & 9…
3. Consider the system \begin{aligned} x + y + z &= 4 \\ 2x + 3y + z &= 11 \\ -x + y - 3z &= 2 \\ 3x + 2y + 4z &= 9 \end{aligned} Solve it by row…
4. The augmented matrix of a system in x, y, z is \left[\begin{array}{ccc|c} 1 & 3 & -1 & 5 \\ 2 & 7 & -4 & 6 \\ -3 & -12 & 9 & c \end{array}\right]…
5. Arjun buys 20 postage stamps for 13 dollars.
6. In the system \begin{aligned} kx + y + z &= 1 \\ x + ky + z &= 1 \\ x + y + kz &= 1 \end{aligned} the letter k appears once in each equation.