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Matrix Meaning

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Nine Eigen

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

A vector ${\bf v}$ is fixed by a matrix if

M{\bf v} = {\bf v}

The vector direction of ${\bf v}$ is fixed if there is some number $\lambda\neq 0$ such that

$$ M{\bf v} = \lambda{\bf v} $$

This resource introduces concepts which appear in the later Further Pure Mathematics A Level modules.