Composition & determinant area
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Flip to reveal answersHow do you find one matrix for 'do A then B'?
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All 8 Flashcards — Composition & determinant area
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Question
How do you find one matrix for 'do A then B'?
Answer
Multiply BA (B on the left): image = B(Ax) = (BA)x. The right-most matrix acts first.
Question
Does the order of composition matter?
Answer
Yes — matrix multiplication is not commutative, so BA ≠ AB in general (different transformations).
Question
What is the determinant of (a b; c d)?
Answer
ad − bc.
Question
How does a matrix change area?
Answer
New area = |det| × old area; |det| is the area scale factor.
Question
What does a negative determinant tell you?
Answer
The transformation reverses orientation — the shape is reflected (flipped over).
Question
What does det = 0 mean for a transformation?
Answer
Area scale factor 0: the plane collapses onto a line/point, so there is no inverse (it can't be undone).
Question
A shape of area 6 is transformed by a matrix with det −4. New area?
Answer
|−4| × 6 = 24 (and the shape is flipped).
Question
What is det(BA) in terms of det A and det B?
Answer
det(BA) = det B × det A.
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Full study notes for Composition & determinant area
Topic 3.9 hub
Matrix transformations (HL only)
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