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**Unformatted text preview: **.0 F05/045/o1 0 Use T.C. 16$ MATH 2451 quiz_05 Exam ble Calculus 1varia Mult' 0
0 Course 25 min .
0 Duration 2016-02-10 (Wed) McCary o
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@W 0 (Last Name) 2016-02-09 19:51 1. O. F05/045/o2 Q l (10 points) Let = ($23: yz). Use a linear approximation from (2) to estimate f Hint: the ex._
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>5 J, Grader Only J, 063 ©®©®©®®®®®Q O. F05/045/0L . . (10 points) Let f = 3’). ' r 0' '-
L 7 7 (a) Find all values of a such that [D f ié singular.- (b) Find all values of a such that; [D f has determinant 1_
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,2é‘x f" fa— : l l Grader 01:11:,r J, .. FOS/O45/O4 . 3. (10 points) Let 2: E C be complex, z = :1: + ﬂy. (a) Show the matrix J = [ has the property J’2 = —I (this should remind you of 2'2 = —1). J: a]
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(b) Notice the function f = (32$: encodes the (C —> C function z t—) 272. Show that matrix product of [D f and J cornnmtes. J 3: “‘0 ‘ r t 1"“ “is” "—3 " P“!
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(c) Notice the function g = encodes the C —) (C function z I—> 2*. Show that the matrix product of . [Dy and J goes not commutex r f f if I, 1* ,7? '7" 4” 7" ND tr! 03
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