Rank and Nullity Worksheet with Answer Key

What's on the worksheet

1. Each row of the table describes an m × n matrix A and its map x Ax.
2. Let A = \begin{bmatrix} 1 & -2 & 0 & 1 & 0 \\ -1 & 2 & 1 & -3 & 0 \\ 2 & -4 & 2 & -2 & 1 \\ -4 & 8 & -1 & -2 & -1 \end{bmatrix}.
3. Let $T:
4. For each description, either give an actual matrix that fits it (and show that it fits), or explain why no matrix can.
5. A 3 × 5 matrix A has rank 2.
6. Let A be an n × n matrix with A² = A, so that A(Ax) = Ax for every x in R^n.