Computing the metric matrix from basis vectors (1,0)^T and (1,1)^T

[narmer]

Homework Statement

If I have a basis: [(1,0)^T, (1,1)^T], how do I compute the metric matrix, which is [(2,1)^T, (1,1)^T]?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

How do you define the "metric matrix". Any linear vector space has a basis but not a "metric matrix".