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國立中央大學 2026 · 考試 · 第 34 題

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The following is an oriented incidence matrix with another orientation setting. What is the result of the multiplication: BBTBB^T (T: transpose)?

B=(1−1−10−1000010−10011)B = \begin{pmatrix} 1 & -1 & -1 & 0 \\ -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 1 & 1 \end{pmatrix}

  • (A)
    (3−1−1−1−1100−1021−1012)\begin{pmatrix} 3 & -1 & -1 & -1 \\ -1 & 1 & 0 & 0 \\ -1 & 0 & 2 & 1 \\ -1 & 0 & 1 & 2 \end{pmatrix}
  • (B)
    (3−1−1−1−1100−102−1−10−12)\begin{pmatrix} 3 & -1 & -1 & -1 \\ -1 & 1 & 0 & 0 \\ -1 & 0 & 2 & -1 \\ -1 & 0 & -1 & 2 \end{pmatrix}
  • (C)
    (3−1−1−1−1200−1111−1012)\begin{pmatrix} 3 & -1 & -1 & -1 \\ -1 & 2 & 0 & 0 \\ -1 & 1 & 1 & 1 \\ -1 & 0 & 1 & 2 \end{pmatrix}
  • (D)
    (3−1−1−1−1200−101−1−10−12)\begin{pmatrix} 3 & -1 & -1 & -1 \\ -1 & 2 & 0 & 0 \\ -1 & 0 & 1 & -1 \\ -1 & 0 & -1 & 2 \end{pmatrix}
  • (E)
    (311011−101−12−100−12)\begin{pmatrix} 3 & 1 & 1 & 0 \\ 1 & 1 & -1 & 0 \\ 1 & -1 & 2 & -1 \\ 0 & 0 & -1 & 2 \end{pmatrix}

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