Practice Flashcards
How do you find the image of a point under a 2×2 matrix?
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All Flashcards in Topic 3.9
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3.9.18 cards
How do you find the image of a point under a 2×2 matrix?
Write the point as a column vector and multiply: matrix on the left, point on the right. (a b; c d)(x; y) = (ax+by; cx+dy).
What is the rotation matrix (anticlockwise about O by θ)?
(cos θ −sin θ; sin θ cos θ).
What is the enlargement matrix, scale factor k, about O?
(k 0; 0 k) — multiplies every distance from O by k.
What is the reflection matrix in the line y = (tan θ)x?
(cos 2θ sin 2θ; sin 2θ −cos 2θ).
Image of (4, 0) under a 90° anticlockwise rotation?
(0 −1; 1 0)(4; 0) = (0, 4).
Which transformation does (−1 0; 0 −1) represent?
A rotation of 180° about the origin: (x, y) → (−x, −y).
How do you transform a whole shape by a matrix?
Transform each vertex (multiply each corner's column vector), then re-join the images.
Which transformation does (1 0; 0 −1) represent?
A reflection in the x-axis (it flips the sign of y only).
3.9.28 cards
How do you find one matrix for 'do A then B'?
Multiply BA (B on the left): image = B(Ax) = (BA)x. The right-most matrix acts first.
Does the order of composition matter?
Yes — matrix multiplication is not commutative, so BA ≠ AB in general (different transformations).
What is the determinant of (a b; c d)?
ad − bc.
How does a matrix change area?
New area = |det| × old area; |det| is the area scale factor.
What does a negative determinant tell you?
The transformation reverses orientation — the shape is reflected (flipped over).
What does det = 0 mean for a transformation?
Area scale factor 0: the plane collapses onto a line/point, so there is no inverse (it can't be undone).
A shape of area 6 is transformed by a matrix with det −4. New area?
|−4| × 6 = 24 (and the shape is flipped).
What is det(BA) in terms of det A and det B?
det(BA) = det B × det A.
Topic 3.9 study notes
Full notes & explanations for Matrix transformations (HL only)
Math AI exam skills
Paper structures, command terms & tips
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