Matrix algebra and linear transformations

Matrix algebra and linear transformations Quiz

Spec 3.1–3 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. A\mathbf{A} is 2×32\times3 and B\mathbf{B} is 3×43\times4. The product AB\mathbf{AB} is

    • A. not defined
    • B. 2×42\times4
    • C. 3×33\times3
    • D. 4×24\times2

  2. 2. The matrix for a stretch of scale factor 33 parallel to the xx-axis is

    • A. (1003)\begin{pmatrix}1&0\\0&3\end{pmatrix}
    • B. (3003)\begin{pmatrix}3&0\\0&3\end{pmatrix}
    • C. (3001)\begin{pmatrix}3&0\\0&1\end{pmatrix}
    • D. (0310)\begin{pmatrix}0&3\\1&0\end{pmatrix}

  3. 3. A rotation through 90∘90^\circ anticlockwise is followed by a reflection in the xx-axis. The combined matrix is

    • A. (0−1−10)\begin{pmatrix}0&-1\\-1&0\end{pmatrix}
    • B. (0110)\begin{pmatrix}0&1\\1&0\end{pmatrix}
    • C. (0−110)\begin{pmatrix}0&-1\\1&0\end{pmatrix}
    • D. (01−10)\begin{pmatrix}0&1\\-1&0\end{pmatrix}

  4. 4. If M\mathbf{M} is a rotation through 45∘45^\circ, the smallest positive nn with Mn=I\mathbf{M}^n=\mathbf{I} is

    • A. 44
    • B. 66
    • C. 1212
    • D. 88

  5. 5. Which matrix represents reflection in the plane x=0x=0?

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

Quiz