(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

17. Let U = f(x; y; 0) : x 2 R; y 2 Rg, E1 = f(x; 0; 0) : x 2 Rg, and E3 = f(0; 0; x) :

x 2 Rg: Are the following assertions true or false? Explain.

(a) U + E1 is a subspace of R3:

(b) U E1 is a direct sum decomposition of U + E1:

(c) U E3 is a direct sum decomposition of R3:

2. Relevant equations

3. The attempt at a solution

I really need to know, from what my teacher told us about it, it seems like a Cartesian Product is adding dimensionality to two sets and that a Direct Sum is just adding every possible vector combination from two vector spaces together. But I really don't know

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# Homework Help: What is the difference between a Cartesian Product and a Direct Sum

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