Question

Linear Algebra: How is {(x1,x2) | |x1|=|x2|} not a subspace of R^2?

Answer 1

Note: that (x1,x2) is a column vector.

Answer 2

Call the set in your question C.

Then among other conditions, C is a subspace if for every a, b in C, a + b in C.

Consider the vectors (1,1) and (1,-1). Both are in C. But
(1,1) + (1,-1) = (2,0)
which is not.

Answer 3

Haha thanks, i'm so narrow-minded when it comes to this.