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X = x(u,v), y = y(u,v) (often one will only get or use the equations in one of these directions) To change the integral to u,vcoordinates, we then have to carry out the three steps A,B,C. °&k* fþ 6 õ)%g"f ,fÝ vfâfïfà û fÿ>á>Ü>Ú>âh h >Þ>Ü>Ý>ä º Ø1* >à>Ü>Ú>äh h f¸f #fØ*(fÔfïfà û fÿ>à>ä>Ú>Þh h >á>ã>Ú>Üh h f÷f¸>Þ>Ü ºg g fûf ,fÝ vfâfïfà û fÜf #fØ*(fÔfïfà û g" v gfófïf¹>Ì 6 õ)%g" ,fÝ vfâfï##äh 0. Solution Any diagonal n n matrix looks like 0 BBB BBB BBB B@ a1 an 1 CCC CCC CCC CA = a1E11 anEnn where Eii is the matrix with entries all 0 except a 1 at the i’th diagonal entry This tells us that (E11;.

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Ma F , W V a U Sa a H a E R b G , L b M a I a c. 3 · ?. Let’s call the new coordinates u and v;.

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