let S be the collection of vectors [x] (2x1 matrix )in R2 that satisfy the given                                            [y] property. In each case, either prove that S forms a subspace of R2 or give a counterexample to show that it does not x>=0,y>=0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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let S be the collection of vectors [x] (2x1 matrix )in R2 that satisfy the given                                            [y]

property. In each case, either prove that S forms a subspace of R2 or give a counterexample to show that it does not

x>=0,y>=0

Expert Solution
Step 1

We can write the set S as S=xy : x0, y0 where x, y. We have to check whether the set S

is a subspace of 2 or not.

A set S is said to be a subspace of a vector space V if the following properties hold:

1. The zero vector lies in the set S.

2. For s1, s2S, we must have s1+s2S.

3. For s1S and scalar a, we must have as1S.

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