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## 'Fix Me or Crush Me' printed from http://nrich.maths.org/

This question becomes much more meaningful and straightforward if
you consider the geometrical interpretation of the action of a
matrix on a vector.

For example, a rotation matrix will leave a line of points
invariant.

A matrix which crushes a vector is a type of 'projection'. Clearly
a projection must send a non-zero vector to the origin.

This problem uses mathematical
concepts found in the later Further Pure Mathematics A
Level modules.