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Back to Determinants and row operations

Exercise 7.4.1

Avg difficulty 3.0

Use row operations to calculate the following determinants:

(a) ∣121232−412∣,(b) ∣21324214−5∣,(c) ∣121231−23−1031232−2∣,(d) ∣141232−23−1033212−2∣.(a)~{}\left|\begin{array}{rrr}1&2&1\\ 2&3&2\\ -4&1&2\end{array}\right|,\quad(b)~{}\left|\begin{array}{rrr}2&1&3\\ 2&4&2\\ 1&4&-5\end{array}\right|,\quad(c)~{}\left|\begin{array}{rrrr}1&2&1&2\\ 3&1&-2&3\\ -1&0&3&1\\ 2&3&2&-2\end{array}\right|,\quad(d)~{}\left|\begin{array}{rrrr}1&4&1&2\\ 3&2&-2&3\\ -1&0&3&3\\ 2&1&2&-2\end{array}\right|.

Selinger, Matrix Theory and Linear Algebra, Determinants, Determinants and row operations, Exercise 7.4.1

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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.