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1998-99 Fall MT1

# 1998-99 Fall MT1 - MATH 260 Midterm 1 Duration 90 ﬁll-11b...

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Unformatted text preview: MATH 260 - Midterm 1 November 21, 1998 Duration : 90 ﬁll-11b. Name : Sectiun : Student No : p)..— can 1 :1 I. 1. (25 131.5.) Determine 11] values of a. such that Iiiesystem [ 2 r; J I: l. a x; _ ‘2 has (i) no sulution. (ii) a unique salutlon, (iii) inﬁnitely many solutions. 2. (25 pls.) Consider the :Vétidi‘ii‘ll = (1, _a;2),'u2 = (4,2,—s),uJ : (4,0,6). u.I =(—2,A3,8)in n3. ‘ , a) Show that R3 = Span{u1, 11:, us). 1)) State the deﬁnition of lineau indcgendence for the. set 5 = {U11 “2, 114}. c) Using the deﬁnitian in part (b), determine whether 5 is a, linearly independent set or not. 1 2 J 4 3 U 2 ‘6 T B 3.(25pus.)let A = 0 019 5 0 0 (3 l 2 0 U 0 I 7 3) Compute detﬁA), b) Compute datudjﬂn. 4. (25 pts.) Given 3 6 0 1 2- o , A = , a = - D D 71 3 6 —l a) Show that (he' matrices A and B are raw equivalént. b} Find an invertible matrix P such that A = PB. ...
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