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Exercise 4.5.8

Avg difficulty 3.0

Using the inverse of the matrix, find the solution to the systems:

  1. [103234102][xyz]=[101],\left[\begin{array}{rrr}1&0&3\\ 2&3&4\\ 1&0&2\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{r}1\\ 0\\ 1\end{array}\right],
  2. [103234102][xyz]=[3−1−2].\left[\begin{array}{rrr}1&0&3\\ 2&3&4\\ 1&0&2\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{r}3\\ -1\\ -2\end{array}\right].

Now give the solution in terms of a,ba,b, and cc to the following:

[103234102][xyz]=[abc].\left[\begin{array}{rrr}1&0&3\\ 2&3&4\\ 1&0&2\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}a\\ b\\ c\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Matrices, Matrix inverses, Exercise 4.5.8

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.