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Math 54 - Spring 2006 - Wagoner - Midterm 1

Math 54 - Spring 2006 - Wagoner - Midterm 1 - Mathematics...

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Mathematics E4 Midterm g1 Spring 2O06 Jack Wagoner IDatructions Write your Datrre, sectio! number, a.nd GSI,s name on vour Blue Book RIGHT NOW. Sbow lour work on problems 2-4, psrl,isl crcdr[ rnay be giveu, but only if the v/ork justifies it. Best wishes on the exa.rn t Problem fl A-oswer Tlue or FaJse in your Blue Book. (A) The fo[owing rnatrix is iu row echelon form. (B) The set coosisting of those Ltuples (o,y,z) safisfyiug the equation x + 2V + 32 : O is a.subspare of ,fiF . (C) The set of_pollnomids p(r) : qoaartlo2r2+osr3 such that y'(o) : 0 is a subepace of P3 .. Here p, (a) denotesthe deriveti ve of p(c). (D) Tbe subaetof lla consisting of all poiDts of the form {r, F, O. 2r} where I is any real number is a subspace of ,#. (E) Ary 2 x 2 matrix .4 setislying the equation _42 +,{ - bI : 0 is invertible. (F)The ooglebetween the two vectors u : (1, 2, -1, t) and o : (g, -1,8, 7) is 90 degrees, (G) Irct ,4 a.nd B be two 5 x 5 matrices . Then 'l:raze(3A + B) :3Trone(A) + Trace(B\ (H) Let.4 be a 2 x 2 matrix. Then Det(gA) = gDet(A).
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