Question

Repeat Problems 8.15and 10.16above for the (u,v)coordinate system if x=2u-v , y=u-2v.

Short answer

The value of matrix is .

Step-by-step solution

Given Information:

The equations are mentioned below.

x=2u

y=u-2v

Definition of covariant basis vector:

A covariant vector, also known as a cotangent vector, has components that co-vary when the basis changes. That is, the components must be converted using the same matrix as the base matrix change.

Find the value:

The equations are mentioned below.

x=2u

y=u-2v

Position vector is,

Covariant basis vectors are mentioned below.

The metric tensor and inverse of metric tensor is given below.

Hence, the value of matrix is.