Linear transformations as matrices

Linear transformations as matrices Quiz

Spec 6.1 · Edexcel International A Level Further Maths: Quiz

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  1. 1. A linear transformation maps (1,0)(1,0) to (3,1)(3,1) and (0,1)(0,1) to (−2,5)(-2,5). Find its matrix.

    • A. (31−25)\begin{pmatrix}3&1\\ -2&5\end{pmatrix}
    • B. (3−215)\begin{pmatrix}3&-2\\ 1&5\end{pmatrix}
    • C. (−2531)\begin{pmatrix}-2&5\\ 3&1\end{pmatrix}
    • D. (3−251)\begin{pmatrix}3&-2\\ 5&1\end{pmatrix}

  2. 2. Find the image of (2,1)(2,1) under (132−1)\begin{pmatrix}1&3\\ 2&-1\end{pmatrix}.

    • A. (5,3)(5,3)
    • B. (3,5)(3,5)
    • C. (5,5)(5,5)
    • D. (1,3)(1,3)

  3. 3. AA has matrix (2001)\begin{pmatrix}2&0\\ 0&1\end{pmatrix} and BB has matrix (0110)\begin{pmatrix}0&1\\ 1&0\end{pmatrix}. Which matrix represents BB followed by AA?

    • A. (0120)\begin{pmatrix}0&1\\ 2&0\end{pmatrix}
    • B. (2001)\begin{pmatrix}2&0\\ 0&1\end{pmatrix}
    • C. (1002)\begin{pmatrix}1&0\\ 0&2\end{pmatrix}
    • D. (0210)\begin{pmatrix}0&2\\ 1&0\end{pmatrix}

  4. 4. Where does any linear transformation send the origin?

    • A. (1,1)(1,1)
    • B. It depends on the matrix
    • C. (0,0)(0,0)
    • D. (1,0)(1,0)

  5. 5. A linear transformation maps (1,0)→(1,1)(1,0)\to(1,1) and (0,1)→(−1,1)(0,1)\to(-1,1). Find the image of (2,3)(2,3).

    • A. (5,−1)(5,-1)
    • B. (−1,5)(-1,5)
    • C. (1,5)(1,5)
    • D. (5,1)(5,1)

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