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Back to The Permutation Expansion

Exercise 1

Avg difficulty 3.0

For this matrix, find the term associated with each 33-permutation.

M=(123456789)M=\begin{pmatrix}1&2&3\\ 4&5&6\\ 7&8&9\end{pmatrix}

That is, fill in the rest of this table.

permutation ϕi\phi_{i} ϕ1\phi_{1} ϕ2\phi_{2} ϕ3\phi_{3} ϕ4\phi_{4} ϕ5\phi_{5} ϕ6\phi_{6}
term m1,ϕi(1)m2,ϕi(2)m3,ϕi(3)m_{1,\phi_{i}(1)}m_{2,\phi_{i}(2)}m_{3,\phi_{i}(3)} 1⋅5⋅91\cdot 5\cdot 9

Hefferon, Linear Algebra, Determinants, The Permutation Expansion, Exercise 1

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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.