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# Fix Me or Crush Me

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Age 16 to 18

Challenge Level

- Problem
- Student Solutions
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Nishad from Rugby High School in the UK found the most general forms of matrices to fix and crush the given vectors:

Can you combine these ideas to get a matrix that both fixes $\bf{F}$ and crushes $\bf{Z}$?

Nishad then moved on to the matrices below and found vectors that they fix and crush.

Nishad used the ideas of eigenvectors and eigenvalues, where $\lambda$ is used to represent an eigenvalue of a matrix. Nishad also used determinants, written $\text{det}(\bf M)$ for a matrix $\bf{M},$ where matrices which crush any vectors satisfy $\text{det}(\bf M)=0.$

*It is also possible to solve this problem without using eigenvalues or determinants - can you find a way?*