Matrices

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Let $A = \begin{pmatrix} -2 & 4 \\ 3 & -3 \end{pmatrix}$, let $I$ be the $2\times 2$ identity matrix, and let $O$ be the $2\times 2$ zero matrix. Compute the trace (the sum of the diagonal entries) of the matrix $AI + 3I + O$.

2. Warm-up

   Let $A = \begin{pmatrix} 4 & 2 \\ 5 & 4 \end{pmatrix}$, let $I$ be the $2\times 2$ identity matrix, and let $O$ be the $2\times 2$ zero matrix. Compute the trace (the sum of the diagonal entries) of the matrix $AI + I + O$.

3. Warm-up

   Let $A = \begin{pmatrix} 4 & -5 \\ 2 & -1 \end{pmatrix}$, let $I$ be the $2\times 2$ identity matrix, and let $O$ be the $2\times 2$ zero matrix. Compute the trace (the sum of the diagonal entries) of the matrix $AI + 5I + O$.

Problems shown under their original terms: Generated (template, solver-computed).