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Back to Symmetric matrices and variance

Exercise 3

Avg difficulty 2.5

Find an orthogonal diagonalization, if one exists, for the following matrices.

  1. [114124−3−1612−161]\begin{bmatrix} 11 & 4 & 12 \\ 4 & -3 & -16 \\ 12 & -16 & 1 \end{bmatrix}.

  2. [102012−2−21]\begin{bmatrix} 1 & 0 & 2 \\ 0 & 1 & 2 \\ -2 & -2 & 1 \\ \end{bmatrix}.

  3. [9333393333933339]\begin{bmatrix} 9 & 3 & 3 & 3\\ 3 & 9 & 3 & 3\\ 3 & 3 & 9 & 3\\ 3 & 3 & 3 & 9\\ \end{bmatrix}.

Austin, Understanding Linear Algebra, §7.1 Symmetric matrices and variance, Exercise 3

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.