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# Nonzero subspace

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I'm attaching a PDF file with a question about finding nonzero subspace along with the property of direct sum. I wonder if anyone who is familiar with Advanced Linear Algebra material and can provide a detail explanation.

#### Solution Preview

Explanation of direct sums and how to find the required subspaces are given in the attached doc file. The question illustrates an important part of the definition for when the direct sum is applied to more than two subsets.

Direct sums of vector subspaces

Find non-zero subspaces of , and of
such that:

(1)
(2)
(3)

First let's recall the definition for the direct sum of two subspaces.

If and are both subspace of vector space V, then:

if and only if ...

#### Solution Summary

This is a question that shows how to find a nonzero subspace with a given direct sum property.

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