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
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
Section: Chapter Questions
Problem 1RQ
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Question
let S be the collection of
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 where . We have to check whether the set S
is a subspace of 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 , we must have .
3. For and scalar a, we must have .
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