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Exercise 7

Avg difficulty 3.0

Find the determinant of this 4 ⁣× ⁣44\!\times\!4 matrix by following the plan: perform Gauss’s Method and look for the determinant to remain unchanged on a row combination, to change sign on a row swap, to rescale on the rescaling of a row, and such that the determinant of the echelon form matrix is the product down its diagonal.

(1202241000−133−114)\begin{pmatrix}1&2&0&2\\ 2&4&1&0\\ 0&0&-1&3\\ 3&-1&1&4\end{pmatrix}

Hefferon, Linear Algebra, Determinants, Exploration, Exercise 7

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.