Eigenvalues and eigenvectors

Eigenvalues and eigenvectors Quiz

Spec 3.1 · Edexcel A-Level Further Maths: Quiz

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  1. 1. Find the eigenvalues of (2112)\begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}.

    • A. 22 and 33
    • B. 11 and 33
    • C. 00 and 44
    • D. 11 and 22

  2. 2. Which is an eigenvector of (1221)\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix} for λ=3\lambda=3?

    • A. (11)\begin{pmatrix} 1 \\ 1 \end{pmatrix}
    • B. (1−1)\begin{pmatrix} 1 \\ -1 \end{pmatrix}
    • C. (21)\begin{pmatrix} 2 \\ 1 \end{pmatrix}
    • D. (13)\begin{pmatrix} 1 \\ 3 \end{pmatrix}

  3. 3. A 2×22\times2 matrix has eigenvalues 22 and 55. Its determinant is

    • A. 77
    • B. 33
    • C. 2.52.5
    • D. 1010

  4. 4. The normalised form of (34)\begin{pmatrix} 3 \\ 4 \end{pmatrix} is

    • A. (34)\begin{pmatrix} 3 \\ 4 \end{pmatrix}
    • B. 17(34)\frac17\begin{pmatrix} 3 \\ 4 \end{pmatrix}
    • C. 15(34)\frac15\begin{pmatrix} 3 \\ 4 \end{pmatrix}
    • D. 125(34)\frac{1}{25}\begin{pmatrix} 3 \\ 4 \end{pmatrix}

  5. 5. A real 2×22\times2 matrix has eigenvalue 3+i3+i. Its other eigenvalue is

    • A. 33
    • B. 3−i3-i
    • C. −3−i-3-i
    • D. i−3i-3

Quiz