# Subspaces of the Vector Space of 2-by-2 Matrices

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#### Solution Preview

10. Let A be a particular vector in R^2x2. Determine whether the following are subspaces of R^2x2:

(a) S_1={B∈R^2x2│BA=0}

To show that a given subset of R^2x2 is a subspace, it suffices to show that it is closed with respect to addition and scalar multiplication. Let B1 and B2 belong to S_1. Then we have B1A=B2A=0, whence ...

#### Solution Summary

We determine whether each of three given subsets of the set of 2 by 2 matrices is a vector subspace.

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