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Matrix algebra

Sums and scalar multiples, the noncommutative product that comes from composing maps, and the identity, transpose, and inverse of a square matrix.

Notes on Diffy Qs: Differential Equations for Engineers, Matrix algebra

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5 exercises

Exercise 101

Add the following matrices

  1. [21011−1]+[534125]\begin{bmatrix} 2 & 1 & 0 \\ 1 & 1 & -1 \end{bmatrix} + \begin{bmatrix} 5 & 3 & 4 \\ 1 & 2 & 5 \end{bmatrix}
  2. [6−237338−12]+[−1−1−3673−94−1]\begin{bmatrix} 6 & -2 & 3 \\ 7 & 3 & 3 \\ 8 & -1 & 2 \end{bmatrix} + \begin{bmatrix} -1 & -1 & -3 \\ 6 & 7 & 3 \\ -9 & 4 & -1 \end{bmatrix}
2.5

Exercise 102

Compute

  1. 2[1234]+3[−1312]2\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + 3 \begin{bmatrix} -1 & 3 \\ 1 & 2 \end{bmatrix}
  2. 3[2−113]−2[21−12]3\begin{bmatrix} 2 & -1 \\ 1 & 3 \end{bmatrix} - 2 \begin{bmatrix} 2 & 1 \\ -1 & 2 \end{bmatrix}
2.5

Exercise 103

Multiply the following matrices

  1. [214344][246335]\begin{bmatrix} 2 & 1 & 4 \\ 3 & 4 & 4 \end{bmatrix} \begin{bmatrix} 2 & 4 \\ 6 & 3 \\ 3 & 5 \end{bmatrix}
  2. [0332−2135−2][662460204]\begin{bmatrix} 0 & 3 & 3 \\ 2 & -2 & 1 \\ 3 & 5 & -2 \end{bmatrix} \begin{bmatrix} 6 & 6 & 2 \\ 4 & 6 & 0 \\ 2 & 0 & 4 \end{bmatrix}
  3. [3412−104−15][025020523616]\begin{bmatrix} 3 & 4 & 1 \\ 2 & -1 & 0 \\ 4 & -1 & 5 \end{bmatrix} \begin{bmatrix} 0 & 2 & 5 & 0 \\ 2 & 0 & 5 & 2 \\ 3 & 6 & 1 & 6 \end{bmatrix}
  4. [−2−25321][0313]\begin{bmatrix} -2 & -2 \\ 5 & 3 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} 0 & 3 \\ 1 & 3 \end{bmatrix}
2.5

Exercise 104

Compute the inverse of the given matrices

  1. [2]\begin{bmatrix} 2 \end{bmatrix}
  2. [0110]\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}
  3. [1235]\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}
  4. [4244]\begin{bmatrix} 4 & 2 \\ 4 & 4 \end{bmatrix}
2.5

Exercise 105

Compute the inverse of the given matrices

  1. [2003]\begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix}
  2. [40005000−1]\begin{bmatrix} 4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -1 \end{bmatrix}
  3. [−1000020000300000.1]\begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 0.1 \end{bmatrix}
2.5

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.