Three-dimensional transformations and 3x3 matrices

Three-dimensional transformations and 3x3 matrices Quiz

Spec 6.1–6 · Edexcel International A Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. Which matrix represents a reflection in the plane z=0z=0?

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

  2. 2. The transformation A\mathbf{A} is applied first, then B\mathbf{B}. The combined matrix is

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

  3. 3. Find ∣102030101∣\begin{vmatrix} 1 & 0 & 2 \\ 0 & 3 & 0 \\ 1 & 0 & 1 \end{vmatrix}.

    • A. 33
    • B. 99
    • C. −3-3
    • D. 00

  4. 4. (AB)−1(\mathbf{AB})^{-1} is equal to

    • A. A−1B−1\mathbf{A}^{-1}\mathbf{B}^{-1}
    • B. B−1A−1\mathbf{B}^{-1}\mathbf{A}^{-1}
    • C. ATBT\mathbf{A}^{\mathrm{T}}\mathbf{B}^{\mathrm{T}}
    • D. 1AB\frac{1}{\mathbf{AB}}

  5. 5. A 3×33\times3 matrix has determinant 00. Which is true?

    • A. it has an inverse
    • B. it is singular
    • C. it is the identity matrix
    • D. its transpose has determinant 11

Quiz