Handwritten Notes on Differential Equations | MAT 475, Study notes of Differential Equations

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w Ae Max arquumeat ostug liveanh af ok Suppose AR iR s cout Uvoes, Qud - $: IR—> Ie" is couh wuously di Rereuk edle, oud for each tEIR sahsGes Be) = AW OO) For IsKsn, \s\sn let Fdenete the K-+h Row LB auch BY aud ES the maces obraiwed fom © by replaciug its k-th rou by its derivative fief aud by the sth wow fi, respect) Note that or each k, 9 > ax: {i | eack You dq Oe Ad ts @ lha cards YY" owas af x] : n 1 and hence det OX = é Oni YD = ag F, \t+ ¢s easily Seeu C iuducheou) Hel S det Bit) = 2. der B* = hajGe, From vahich if Allows that for all telR det BA) = det Bla. exp [HAG ds,