Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 5 / b / iv

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- Solution iv

Solution

The

j

th column of

A E

is

A (E e_{j})

. The permutation matrix fixes

e_{1}, e_{2}

and interchanges

e_{3}, e_{4}

, so these columns are

A e_{1}, A e_{2}, A e_{4}, A e_{3}

. They are exactly the first, second, fourth and third columns of

A

. Thus right multiplication by $E$ interchanges columns three and four, leaving the others unchanged.

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