Linear transformations

Linear transformations Quiz

Spec C3 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Which matrix represents a reflection in the line y=xy=x?

    • A. (0−110)\begin{pmatrix}0&-1\\1&0\end{pmatrix}
    • B. (0110)\begin{pmatrix}0&1\\1&0\end{pmatrix}
    • C. (100−1)\begin{pmatrix}1&0\\0&-1\end{pmatrix}
    • D. (−1001)\begin{pmatrix}-1&0\\0&1\end{pmatrix}

  2. 2. Find the image of (2,−1)(2,-1) under (2003)\begin{pmatrix}2&0\\0&3\end{pmatrix}.

    • A. (4,3)(4,3)
    • B. (2,−3)(2,-3)
    • C. (−4,3)(-4,3)
    • D. (4,−3)(4,-3)

  3. 3. An enlargement of scale factor 33 about the origin is followed by a reflection in the xx-axis. Find the matrix of the combined transformation.

    • A. (300−3)\begin{pmatrix}3&0\\0&-3\end{pmatrix}
    • B. (−3003)\begin{pmatrix}-3&0\\0&3\end{pmatrix}
    • C. (3003)\begin{pmatrix}3&0\\0&3\end{pmatrix}
    • D. (1300−13)\begin{pmatrix}\frac13&0\\0&-\frac13\end{pmatrix}

  4. 4. Which matrix represents reflection in the plane x=0x=0 in three dimensions?

    • A. (1000−10001)\begin{pmatrix}1&0&0\\0&-1&0\\0&0&1\end{pmatrix}
    • B. (10001000−1)\begin{pmatrix}1&0&0\\0&1&0\\0&0&-1\end{pmatrix}
    • C. (−100010001)\begin{pmatrix}-1&0&0\\0&1&0\\0&0&1\end{pmatrix}
    • D. (−1000−1000−1)\begin{pmatrix}-1&0&0\\0&-1&0\\0&0&-1\end{pmatrix}

  5. 5. Transformation PP has matrix P\mathbf{P} and QQ has matrix Q\mathbf{Q}. What is the matrix for PP followed by QQ?

    • A. PQ\mathbf{P}\mathbf{Q}
    • B. QP\mathbf{Q}\mathbf{P}
    • C. P+Q\mathbf{P}+\mathbf{Q}
    • D. P−1Q\mathbf{P}^{-1}\mathbf{Q}

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