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Matrix theory of subsets

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This is a subset of R3. What is it, geometrically? (Give a brief description)
Show that S is a subspace of R3.
Find a matrix A such that...


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Notice that

1 5 0
1 0 -5
0 0 ...

Solution Summary

This provides an example of geometrically describing a subset, showing that it is a subspace, and finding a matrix with a given eigenvalue.