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111-2005&amp;2006-1-M10-Nov2005_2

# 111-2005&amp;2006-1-M10-Nov2005_2 - Kuwait University...

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Unformatted text preview: Kuwait University MATH 111 Nov 24., 2005 Math. Dept. First Midterm Test Duration 90 minutes The use of calculators and all mobile communication equipment (mobiles or pagers and others) are not allowed during the exam. 5 l ‘2 O l l 1. a points) Let A = 1 O O and C 2 1 2 2 »\ 2 3 4 l 1 3 3 'l (a) if possible, ﬁnd .4-1 and 01. 9 :7? 6 y» (b) Use (b) to solve the linear system AX = 2 . y 2 V01 points) (a) Consider A = l i: i J. Find the values of a such that A is row L . ‘ equivalent to 12. :3) (b) Find all matrices X such that BfX = X52 Where B 3 [(1] i J @ (4 points) Find all the values of a for whichtheresultinglinear system has a ._., ,V,,w_v, H if: ( ) no solution, (b) a unique solution“, (c) inﬁnitely many solutions “351:? V 33: + 31/ + z + t : 5 7a \ “Nip? 2:6 + 2y + z + t = 4 g? V \ ”a! by; m+y+z+t+u=_ 3' 90\ f"? ‘\\‘\ :c —l— y = (1+1 1’ / ”>/ v» . y _ 0.1 C12 G3 251 + C1 252 -i- C2 2133 + C3 @2 points) If ()1 b2 b3 = 1 ﬁnd Sal — bl 30.2 — b2 3&3 "— 53 giving reasons C1 (32 C3 :11 0.2 (13 ' ' for your answer. 5. (2 points) if AB and C are n X n. matrices and BA : AC 2 In show that B = . 6. (2 points) If AB = 0 then either A is singular or B is singular. 7. (6 points) Answer each of the following as true or false (justify your answer): fair-C: a) The sign of the term a14a22a31a43 in the expansion of the determinant of a 4 X 4 matrix is minus. "Wag, ' ' A is an n x n symmetric and skew—symmetric matrix then A = Or; (the ;x). _ ' a 3 x 2 matrix then AX = O has a non-trivial solutions; if}? \ ‘duct of two scalar matrices is a scalar matrix. no like" (- OO 99 I A B 2 o :2) Mr (AB) : Ga-uirmymm : J ff‘ﬁ—“M W - ~—~—:—f m (if) hi/ "waSw’é/mw lo) T T‘ i «v.2. (08») A '3 x—‘—'A :)2A:“D'“—-),ﬁ-«(I (4 \ 5' C) Faﬂ CO (5- __‘( a": \ L W E?! R PE) Coquc/x me VQQ A 2 E " 0; f E d {,5 , 3; >T‘oue. (.0 5?) .) (“IE Mtg—5:“ 2 at, T- I ) S5 w E : (“L HLL (‘39-1 k V! ...
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111-2005&amp;2006-1-M10-Nov2005_2 - Kuwait University...

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