Let S be the subset of R3 defined by S = {( x3 Note that S contains the zero vector 0 but it is not a subspace of R³ and

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Let S Be The Subset Of R3 Defined By S X3 Note That S Contains The Zero Vector 0 But It Is Not A Subspace Of R And 1 (302.83 KiB) Viewed 51 times

Let S be the subset of R3 defined by S = {( x3 Note that S contains the zero vector 0 but it is not a subspace of R³ and you must prove this below by providing an example that demonstrates it is either not closed under vector addition or not closed under scalar multiplication or both. x1 You are given that one vector in S is x2 --}. € R³ :|x₁|- |x2| - |x3|= 0 4 --(0) u= 3 and you must use this vector in your counterexample or counterexamples. 1. If S is closed under vector addition, enter the word "closed" in the box below. If it is not closed under vector addition, find a non-zero vector v ES such that u + v is not in S and enter this in the box below in Matlab syntax. • P 2. If S is closed under scalar mulitplication, enter the word "closed" in the box below. If it is not closed underscalar multiplication, find a scalar A E R such that Au is distinct from u and not in S and enter this in the box below.