Need help with 1 Please help Thanks in advanceSolution1 Yes

Need help with #1. Please help. Thanks in advance!

Solution

1. Yes, H is a subspace of 2 dimentional verctor space of Real numbers.

Because, any vector space can be represented as linear transformation from another vector space.

Eg: f(x + y) = f(x) + f(y) and f(a · x) = a · f(x) for all x and y in V

In this case, H is mapped by the linear combination of x and y. So it is also a vector space in R. As it has two different transformation operations, resulting in two dimentional Vector. So it is a vector space in R^2.