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Linear Algebra: Using Scalar Multiplication to prove that a set is within R2?
I'm studying for a linear algebra test, and I'm having a bit of trouble proving that a set is closed under Scalar Multiplication (I've got Vector Addition down fine).
Here's my example:
Show W = {(x, y) in R^2 : xy = | xy | } is closed under Scalar Multiplication.
I have this so far:
Let λ be a scalar.
Let the vector u = (u1, u2) in W, i.e. u1u2 = | u1u2 |
If you can help me figure out what's next, I will greatly appreciate it. Hopefully this will help me figure out subsequent problems. Thanks.
1 Answer
- 1 decade agoFavorite Answer
closed under scalar multiplication simply means that if you multiply by a scalar (k) and you get an element of W then its closed in scalar multiplication...
if u is an element of w
ku is also an element means that w is closed under scalar multiplication
