Rank Worksheet with Answer Key

What's on the worksheet

1. Find the rank of each matrix using at most two row operations.
2. Let A = \begin{bmatrix} 1 & -2 & -2 & -1 & -3 \\ 3 & -6 & -5 & -2 & -6 \\ 3 & -6 & -3 & 0 & 0 \end{bmatrix}.
3. Let M = \begin{bmatrix} k & 2 & 4 \\ 1 & k - 1 & 2 \\ 2 & 2 & k + 2 \end{bmatrix}.
4. For each description, give an example or explain why none exists.
5. Amara checks the masses of three carabiner models at the climbing-gear shop where she works; the unknown masses of one carabiner of each model are…
6. Let A be an m × n matrix and B an m × p matrix, and suppose every column of B is a linear combination of the columns of A.