Final answer:
The standard basis for R^6 consists of six vectors, where each vector has one component of 1 and the rest are 0, representing the axes of the six-dimensional space.
Step-by-step explanation:
The standard basis for a vector space, specifically for R6, consists of six vectors, each having one component equal to 1 and the rest equal to 0. The standard basis vectors for R6 are written as:
- e1 = (1, 0, 0, 0, 0, 0)
- e2 = (0, 1, 0, 0, 0, 0)
- e3 = (0, 0, 1, 0, 0, 0)
- e4 = (0, 0, 0, 1, 0, 0)
- e5 = (0, 0, 0, 0, 1, 0)
- e6 = (0, 0, 0, 0, 0, 1)
Each of these vectors represents one axis of the six-dimensional space, and any vector in R6 can be represented as a linear combination of these basis vectors.