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Exercise 102

Avg difficulty 2.5

For which xx are the following matrices singular (not invertible):

  1. [131x]\begin{bmatrix} 1 & 3 \\ 1 & x \end{bmatrix}
  2. [3x13]\begin{bmatrix} 3 & x \\ 1 & 3 \end{bmatrix}
  3. [x33x]\begin{bmatrix} x & 3 \\ 3 & x \end{bmatrix}
  4. [x10140162]\begin{bmatrix} x & 1 & 0 \\ 1 & 4 & 0 \\ 1 & 6 & 2 \end{bmatrix}

Lebl, Notes on Diffy Qs, §10.6 Determinant, exercise 102

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.