Maps in the plane

Task number: 2563

Determine matrices of the following linear maps in the plane (\(\mathbb R^2\to \mathbb R^2\)) with respect to the canonical base \(K\).

  • Variant 1

    the axis symmetry w.r.t. to axis of the 1st and the 3rd quadrant.

  • Variant 2

    counterclockwise rotation by \(90^\circ\) around the origin (the first axis is vertical, the second horizontal).

  • Variant 3

    counterclockwise rotation by \(\alpha\) around the origin.

  • Variant 4

    the projection to the first coordinate \(p_1:(x,y)\to(x,0)\)

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
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