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Year 1 of the computer science course of the University of Oxford

Past exam of the year 1 of the computer science course of the University of Oxford

2016

Digital systems, linear algebra, introduction to formal proof (resit)

Undo each <elementary row operation>: divide row 3 by 3, add 3 times row 2 to row 4, and repeat the same swap. Hence
$$
\boxed{E_s^{-1}=\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&1/3&0\\0&0&0&1\end{pmatrix},\quad E_a^{-1}=\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&3&0&1\end{pmatrix},\quad E_p^{-1}=E_p.}
$$
Multiplying each inverse by its original matrix gives the <identity matrix>.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 5 / b / Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 5 / b / Solution

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