Homogeneous Systems and Solutions in Parametric Vector Form Worksheet with Answer Key

What's on the worksheet

1. Find every solution of each homogeneous system in parametric vector form, and say whether the solution set is \0\, a line, a plane, or larger.
2. Let A = \begin{bmatrix} 1 & 3 & 0 & 2 \\ -3 & -9 & 1 & -8 \\ 2 & 6 & -3 & 10 \end{bmatrix}, \qquad \mathbf{b} = \begin{bmatrix} -4 \\ 8 \\ 4…
3. Let p = (1, 1, 1, 2), v_1 = (2, -1, 1, 0) and v_2 = (-1, 3, 0, 1) in R^4.
4. Let A = \begin{bmatrix} 1 & 2 & 1 & 2 \\ 2 & 4 & 3 & 3 \end{bmatrix}, \qquad \mathbf{b} = \begin{bmatrix} 3 \\ 7 \end{bmatrix}. Three students…
5. Isabel mixes potting soil for a batch of seedling trays from three ready-made blends.
6. Let A be an m × n matrix.