 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Physics course of the University of Oxford

Year 1 of the physics course of the University of Oxford

Mathematical methods I course of the University of Oxford

Past exam of the mathematical methods I course of the University of Oxford

2015

Repeated substitution in the <affine iteration> gives
$$
x_k=M^{k-1}x_1+(I+M+\cdots+M^{k-2})c.
$$
Therefore the required <matrix polynomials> are
$$
\boxed{f(M)=M^{k-1},\qquad g(M)=\sum_{j=0}^{k-2}M^j.}
$$
These formulas do not require an inverse. If $I-M$ is an <invertible matrix>, multiplying the finite geometric sum by $I-M$ gives $g(M)=(I-M^{k-1})(I-M)^{-1}$.

Solution

Past exam of the mathematical methods I course of the University of Oxford / 2015 / 13 / a / ii / Solution

Past exam of the mathematical methods I course of the University of Oxford / 2015 / 13 / a / ii / Solution

 Ancestors (13)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematical methods I course of the University of Oxford / 2015 / 13 / a / ii / Solution

 Ancestors (13)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)