Consider the system (a) Show that, near the point (x1, x2, y1, y2, y3) = (1, 0,...

Consider the system

(a) Show that, near the point (x1, x2, y1, y2, y3) = (1, 0,−1, 1, 2), it is possible to solve for y1, y2, y3 in terms of x1, x2.

(b) From the result of part (a), we may consider y₁, y₂, y₃ to be functions of x₁ and x₂. Use implicit differentiation and the chain rule to evaluate ∂y1/∂x1 (1, 0), ∂y₂ /∂x1 (1, 0), and ∂y₃ /∂x₁ (1, 0).