Could anyone provide an example of a nonempty subset $U$ of $R^2$ such that $U$ is closed under scalar multiplication, but $U$ is not a subspace of $R^2$
Linear Algebra – Example of a Nonempty Subset Closed Under Scalar Multiplication but Not a Subspace
linear algebra
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Best Answer
The cross.
(More precisely, the union of the $x$-axis and $y$-axis.)