Lesson Plan

Describe how a $2 \times 2$ matrix transforms the plane by tracking where the standard basis vectors go.

Sketch the image of the unit square under a given $2 \times 2$ transformation.

Interpret $|\det(A)|$ as the factor by which $A$ scales areas.

Explain the geometric meaning of the sign of $\det(A)$: positive = orientation preserved; negative = orientation reversed.

Explain why $\det(A) = 0$ corresponds to a non-invertible (area-collapsing) transformation and connect this to VM.C.10.

HSN.VM.C.12