Determinants & inverses

What the problems look like

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

1. Warm-up

   A linear transformation of the plane has matrix $A = \begin{pmatrix} -3 & 3 \\ 2 & -4 \end{pmatrix}$. Compute $\det(A)$; the transformation is invertible exactly when this value is nonzero.

2. Warm-up

   A linear transformation of the plane has matrix $A = \begin{pmatrix} -1 & 3 \\ 1 & 4 \end{pmatrix}$. Compute $\det(A)$; the transformation is invertible exactly when this value is nonzero.

3. Warm-up

   A linear transformation of the plane has matrix $A = \begin{pmatrix} 3 & -5 \\ 3 & -6 \end{pmatrix}$. Compute $\det(A)$; the transformation is invertible exactly when this value is nonzero.

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