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6. (For this problem you will need to remind yourself how to multiply 2 x 2 matrices.) Consider the changes of coordinates 'I' from {(s,t)

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6. (For this problem you will need to remind yourself how to multiply 2 x 2 matrices.) Consider the changes of coordinates 'I' from {(s,t) : 3,t > 0} to {(u,v) : u E Rm 6 R} and (I) from {(u,v) : u E R1) ER} to {(x,y) : a: E Ry 6 1R} given by: '1! :u(s, t) = s4 6321:2 +154 v(s, t) = 4331: 43153; (I) :x(u, v) : e\" cos(v) y(u, v) = e" sin(v). (1) Compute 3:3, mt, ys and yt. (ii) Compute the Jacobian matrices %, %, and %. (iii) Evaluate the Jacobian matrices above at the point 3 = 1, t = 1. (iv) Compute the product of matrices below: (38:33\" = 1)) (2221:?\" = = 1)) what did you notice

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