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Mathematics for AI, Problem Set: Linear Algebra

Let L be the z-axis and P the xy-plane in ℝ³.
a) is the union of P with L a vector space in ℝ³?

Answer 1

The union of P with L is not a vector space in ℝ³.

Step-by-step explanation:

The union of P with L is not a vector space in ℝ³. In order for a set to be a vector space, it needs to satisfy certain properties such as closure under addition and scalar multiplication. However, the union of P with L does not satisfy these properties.