Final answer:
Let V be the set of all vectors of the form u = (a, b, c) where a, b, and c are real numbers. Find vectors u and v in V such that u = (1, 2, 3) and v = (4, 5, 6).
Step-by-step explanation:
In the given question, the set V is defined as the set of all vectors of the form u = (a, b, c), where a, b, and c are real numbers. This means that any vector in V can be represented as (a, b, c), where a, b, and c can take any real values.
To find vectors u and v in V, we can choose specific values for a, b, and c. In this case, let u = (1, 2, 3) and v = (4, 5, 6). These vectors satisfy the condition of being in the set V, as they are of the form (a, b, c) with real number components.
In the context of vector spaces, the set V is described as all vectors of the form u = (a, b, c), where a, b, and c can take on any real values. This is a general representation of a three-dimensional vector. To find specific vectors u and v in V, we can assign values to the components. Choosing u = (1, 2, 3) and v = (4, 5, 6) satisfies the conditions, as both vectors are in the form (a, b, c) with real number entries.
This means that u and v belong to the set V. The arbitrary nature of the parameters a, b, and c in the set V allows for an infinite number of vectors that can be represented in this form. The selected values for u and v are merely one example that fulfills the given criteria.