 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2022

Paper 1

Move the first $n-k$ columns of
$$
A=\begin{pmatrix}0&M\\N&0\end{pmatrix}
$$
past its last $k$ columns. This requires $k(n-k)$ column interchanges and produces the <block diagonal matrix>
$$
\begin{pmatrix}M&0\\0&N\end{pmatrix}.
$$
Each interchange reverses the determinant's sign, so part (a) gives
$$
\boxed{\det A=(-1)^{k(n-k)}(\det M)(\det N)}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 1F / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 1F / b / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 1F / b / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)