INSTRUCTOR: Find the Jacobian of the transformation given in the previous checkpoint. That is t of u comma v equal to open parentheses u plus v comma 3 v close parentheses. Now, the Jacobian is a matrix made up of partial derivatives.

So in our case, this would be the x component with respect to u, and the y component with respect to u as derivatives as our first row. And our second row would be the x component with respect to v, and the y component with respect to v. And then we find the determinant of that matrix.

So in this case, j of u comma v, Jacobian is the determinant of the matrix 1, 0, 1, 3. That was two elements in the numerator, 1 and 0 and two elements in the-- Not the numerator, in the first row was 1 and 0. And the second row is 1 in 3. Now, the determinant of that matrix is 3.