Determinants and inverses of 2x2 matrices

Determinants and inverses of 2x2 matrices Quiz

Spec 5.4–5 · Edexcel International A Level Further Maths: Quiz

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  1. 1. Find det⁡(3524)\det\begin{pmatrix}3&5\\ 2&4\end{pmatrix}.

    • A. 2222
    • B. 22
    • C. −2-2
    • D. 88

  2. 2. For which value of kk is (2k36)\begin{pmatrix}2&k\\ 3&6\end{pmatrix} singular?

    • A. 22
    • B. 33
    • C. 66
    • D. 44

  3. 3. Find the inverse of (3152)\begin{pmatrix}3&1\\ 5&2\end{pmatrix}.

    • A. (2−1−53)\begin{pmatrix}2&-1\\ -5&3\end{pmatrix}
    • B. (2153)\begin{pmatrix}2&1\\ 5&3\end{pmatrix}
    • C. (−215−3)\begin{pmatrix}-2&1\\ 5&-3\end{pmatrix}
    • D. (3−1−52)\begin{pmatrix}3&-1\\ -5&2\end{pmatrix}

  4. 4. Which expression equals (AB)−1(\mathbf{AB})^{-1}?

    • A. A−1B−1\mathbf A^{-1}\mathbf B^{-1}
    • B. AB\mathbf{AB}
    • C. B−1A−1\mathbf B^{-1}\mathbf A^{-1}
    • D. −BA-\mathbf{BA}

  5. 5. Find the inverse of (4−213)\begin{pmatrix}4&-2\\ 1&3\end{pmatrix}.

    • A. 114(3−214)\frac1{14}\begin{pmatrix}3&-2\\ 1&4\end{pmatrix}
    • B. 114(32−14)\frac1{14}\begin{pmatrix}3&2\\ -1&4\end{pmatrix}
    • C. 114(42−13)\frac1{14}\begin{pmatrix}4&2\\ -1&3\end{pmatrix}
    • D. 110(32−14)\frac1{10}\begin{pmatrix}3&2\\ -1&4\end{pmatrix}

Quiz