ECO 3145: Spring/Summer 2022 Quiz 2
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ECO 3145: Spring/Summer 2022
Quiz 2
I) Consider the equation
G(x, y) = x2 − 3xy + y3 + 1 = 0
1. Are the conditions of the implicit function theorem satisfied at the point (x0 , y0 ) = (3, 2)? Justify your answer. 3 marks
2. Find the value of at (x0 , y0 ) = (3, 2). 2 marks
II) Consider the following three equations
xy − 2w = 0
y − 2w2 − z = 0
w2 + z2 − zw = 0
1. Determine the total differential of the system. 2 marks
2. Represent the total differential of the system in matrix form JV = Udz,
where J is the Jacobian matrix , V = (dx dy dw) and U a vector. 2 marks
3. Are the conditions of the implicit function theorem satisfied at the point (x, y, w; z) = ( , 4, 1, 2)? Justify your answer. 3 marks
4. Using the Cramer’s rule, find the expressions of , and at (x, y, w; z) = ( , 4, 1, 2). 3 marks
2022-06-10