Obtain the Jacobian matrix for each of the following mappings:
a) y1 = 5x1 + 2x2, y2 = 2x1 + 3x2.
b) y1 = 2x12 + x22, y2 = 3x1x2.
c) y1 = x1x2x3, y2 = x12x3.
d) u = x cos y, v = x sin y,w = x2.
e) w = x2yz.
f) w = x2 + y2 – z2.
g) x = t2, y = t3, z = t4.
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