# Vector spaces

Please see attachment.

The set of elements belonging to R^2 is usually denoted as {(a, b) | a, b ∈ R}. Combining elements within this set under the operations of addition and scalar multiplication should use the following notation:

Addition Example: (-2, 10) + (-5, 0) = (-2 - 5, 10 + 0) = (-7, 10)

Scalar Multiplication Example: -10 × (1, -7) = (-10 × 1, -10 × -7) = (-10, 70), where -10 is a scalar.

Assignment:

Write an explanation of vector space where you:

1) Provide a mathematical definition for a vector space.

2) Indicate whether R^2 is a vector space.

* Justify assertions by applying the provided mathematical definition for a vector space.

3) Determine whether R^2 is spanned by (1, 1) and (3, 2) (show all work).

4) Define a nontrivial subspace of R^2 (show all work).

https://brainmass.com/math/linear-algebra/linear-algebra-vector-space-problems-419554

#### Solution Summary

Vector spaces are clarified in this solution.