3.9 Matrix transformations

3.9 Matrix transformations Quiz

IB Maths: Applications and Interpretation HL: Quiz

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5 questions, one answer each

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  1. 1. Which matrix represents an enlargement with scale factor 33, centre the origin?

    • A. (3001)\begin{pmatrix}3 & 0 \\ 0 & 1\end{pmatrix}
    • B. (1003)\begin{pmatrix}1 & 0 \\ 0 & 3\end{pmatrix}
    • C. (3003)\begin{pmatrix}3 & 0 \\ 0 & 3\end{pmatrix}
    • D. (0330)\begin{pmatrix}0 & 3 \\ 3 & 0\end{pmatrix}

  2. 2. Find the image of (4,1)(4,1) under (2103)\begin{pmatrix}2 & 1 \\ 0 & 3\end{pmatrix}.

    • A. (93)\begin{pmatrix}9 \\ 3\end{pmatrix}
    • B. (83)\begin{pmatrix}8 \\ 3\end{pmatrix}
    • C. (87)\begin{pmatrix}8 \\ 7\end{pmatrix}
    • D. (39)\begin{pmatrix}3 \\ 9\end{pmatrix}

  3. 3. A shape of area 55 is transformed by (4123)\begin{pmatrix}4 & 1 \\ 2 & 3\end{pmatrix}. What is the area of the image?

    • A. 1010
    • B. 55
    • C. 1515
    • D. 5050

  4. 4. What transformation does (0110)\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix} represent?

    • A. Reflection in the xx-axis
    • B. Reflection in the line y=xy=x
    • C. Rotation of 90∘90^\circ anticlockwise
    • D. Reflection in the yy-axis

  5. 5. Transformation with matrix P\mathbf{P} is applied first, then the one with matrix Q\mathbf{Q}. The single matrix is

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

Quiz