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Precalculus Flashcards: Using 2x2 Matrices For Plane Transformations

Study Using 2x2 Matrices For Plane Transformations in Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

QUESTION

For A=(0−110)A=\begin{pmatrix}0&-1\\1&0\end{pmatrix}, what is the image of (x,y)(x,y)?

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ANSWER

(−y, x)(-y,\,x). This matrix rotates by 90°90° counterclockwise.

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Precalculus: Matrix Operations & Applications

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This deck focuses on Using 2x2 Matrices For Plane Transformations, giving you a quick way to review the definitions, rules, and examples that matter most for Precalculus.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Practice questions

1 of 44Practice questions for this set
For the transformation matrix R=(0−110)R=\begin{pmatrix}0&-1\\1&0\end{pmatrix}, which represents a rotation of the coordinate plane, what is the image of the point (3,4)(3,4) under T(v)=RvT(\mathbf{v})=R\mathbf{v}? (This transformation has det⁡(R)=1\det(R)=1, so areas are preserved.)
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