Kernel Worksheet with Answer Key

What's on the worksheet

1. Let A = \begin{bmatrix} 1 & 0 & 1 & -3 \\ -3 & 1 & -2 & 10 \\ 3 & 2 & 5 & -7 \end{bmatrix}, \quad \mathbf{v}_1 = \begin{bmatrix} -1 \\ -1 \\ 1 \\ 0…
2. Let A = \begin{bmatrix} 1 & 3 & 1 & 0 & 1 \\ 2 & 6 & 0 & 1 & 7 \\ -1 & -3 & 1 & 1 & 0 \\ 1 & 3 & -1 & 2 & 9 \end{bmatrix}.
3. Decide whether each map is one-to-one.
4. Find the kernel of each map and describe it geometrically.
5. Ryan's upholstery shop orders sample books of fabric swatches from a supplier that makes four kinds of book.
6. Let A be an m × n matrix for which x Ax is one-to-one, and let B be an n × p matrix.