Matrix arithmetic

Matrix arithmetic Quiz

Spec C1–C2 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. A 3×23\times2 matrix is multiplied by a 2×42\times4 matrix. What is the order of the product?

    • A. 2×22\times2
    • B. 3×43\times4
    • C. 2×32\times3
    • D. 4×34\times3

  2. 2. Find (1203)\begin{pmatrix}1&2\\0&3\end{pmatrix} ++ (−1041)\begin{pmatrix}-1&0\\4&1\end{pmatrix}.

    • A. (0242)\begin{pmatrix}0&2\\4&2\end{pmatrix}
    • B. (−1003)\begin{pmatrix}-1&0\\0&3\end{pmatrix}
    • C. (22−42)\begin{pmatrix}2&2\\-4&2\end{pmatrix}
    • D. (0244)\begin{pmatrix}0&2\\4&4\end{pmatrix}

  3. 3. A\mathbf{A} is 2×32\times3 and B\mathbf{B} is 3×33\times3. Which of the products is defined?

    • A. AB\mathbf{AB} only
    • B. BA\mathbf{BA} only
    • C. Both AB\mathbf{AB} and BA\mathbf{BA}
    • D. Neither

  4. 4. For A=(2134)\mathbf{A}=\begin{pmatrix}2&1\\3&4\end{pmatrix} and the identity matrix I\mathbf{I}, what is AI\mathbf{AI}?

    • A. I\mathbf{I}
    • B. A\mathbf{A}
    • C. O\mathbf{O}
    • D. 2A2\mathbf{A}

  5. 5. If AB=O\mathbf{AB}=\mathbf{O}, the zero matrix, what can be concluded?

    • A. A=O\mathbf{A}=\mathbf{O}
    • B. B=O\mathbf{B}=\mathbf{O}
    • C. It is possible that neither A\mathbf{A} nor B\mathbf{B} is O\mathbf{O}
    • D. AB=BA=I\mathbf{AB}=\mathbf{BA}=\mathbf{I}

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