Transformations (AQA A-Level Further Maths): Quizzes

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Transformations
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When applying a transformation matrix T\mathbf{T} to a vector x\mathbf{x}, which is correct?

Tx\mathbf{T}\mathbf{x} (pre-multiplication)

Which matrix represents a reflection in the y-axis?

(−1001)\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}

In the rotation matrix (cos⁡θ−sin⁡θsin⁡θcos⁡θ)\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}, where does cos⁡θ\cos\theta appear?

On the leading diagonal

Which matrix stretches with scale factor kk parallel to the x-axis?

(k001)\begin{pmatrix} k & 0 \\ 0 & 1 \end{pmatrix}

What is the key difference between a stretch and an enlargement?

Stretch changes one direction only

What do the columns of a transformation matrix represent?

Images of the basis vectors

If transformation A\mathbf{A} is followed by B\mathbf{B}, which matrix represents the combined transformation?

BA\mathbf{BA}

In a 3D rotation matrix, what happens to the coordinate of the axis being rotated around?

It stays unchanged

What condition must an invariant point satisfy?

Tx=x\mathbf{Tx} = \mathbf{x}

What distinguishes an invariant line from a line of invariant points?

Points map to other points on same line

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