Final answer:
The dimension of the vector subspace V = span(e2, e1 - 2e2, 3e1) can be determined by finding a basis for V and counting the number of basis vectors.
Step-by-step explanation:
The dimension of the vector subspace V = span(e2, e1 - 2e2, 3e1) can be determined by finding a basis for V and counting the number of basis vectors.
To find the basis, we need to determine if the vectors e2, e1 - 2e2, and 3e1 are linearly independent or dependent. We can do this by setting up a system of equations and solving for the coefficients that make the linear combination equal to zero.
The vector subspace V will have a dimension equal to the number of linearly independent vectors in the basis. If the vectors are linearly independent, the dimension will be 3. If they are dependent, the dimension will be less than 3.