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111-2006&amp;2007-1-M10-November2006_2

# 111-2006&amp;2007-1-M10-November2006_2 - gawk LINEAR...

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Unformatted text preview: gawk ._.... ..,____ LINEAR ALGEBRA "(Malta 111) First Mid-Term Test November 2, 2006 Duration 90 minutes Calculators, Mobile phones, Pagers and all other mobile communication equipments are NOT allowed. Answer the following questions: 1—1 4 023 1.[3pts.]LetA—[O 1_2([andB=[2 2 5]. a) If possible compute B2); 53A and BAT. ”Express the third column of the product BTA as a linear combination of columns of ET. 2. [6 pts.[ Consider the following linear system X :C + By + 32 : 13 23 + 5g + (4-+3k)z = 23. 23: + 7y + (2k2+9)z : k+30 (3) Find all values of k for which the given linear system has a solution. (b) Solve the system for k = —1. 1 l 2 f‘ . [4 pts. LetA: 1 a 3 . ’ 1 1 (1 Find all values of a such that A is nonsingular. iii l5 “MN” H i (b) Find IAI, when a. 2 3. A’V-I: 4. [6 pts.[ Answer each of the following as True or False (justify your answer). ﬁh) If A and B are n we upper triangular matriees, then (A—B)(A+B) = A2 — Ba. P figxb) The number of inversions of the permutation 463251 is l1. £114.— R,“ (c) If A is a 3 x 3 skew-symmetric matrix, then [AT/ll > O. (3.9a) If U1 and U2 are solutions of AX : B (B a 0), then 2Ul — U2 is a solution for i- AX : o. Lia-:23 1 1 ‘2 2 —2 5 ‘ 5. [6 pts.] Let A 2 1 2 3 and B = 7 1 10 be two nonsingular matrices. [K 1 2 4 5 —l 5 ﬂat/ind A’i. Find a matrix C for which CA 1 .1 —.(‘A(B 1T) ) 1 4- A‘l. ET”? I; / ﬂ“! 91‘ M’ I” :‘Ul‘sfnyM/jw ﬂﬂ/r I"; uni‘qng ’x 57%? I: . PE?!— LE/ ’4 £141 1ch?! g " e1” 8-66 =1nC :91 I am“ mm a" (3,) (3,0413) :Ac'aﬂ, (53 M 3. [29:3 2:14/ fig) 0 O 9133;“: QH’II 22+: 914/ (D ’ 0 C K I) {‘5 2 /; 3; 4+ a: 9(a) 1],} Hg @Q g:/, ;5 [0:5 /3Z “(2 3,55,34622 O CO 0 2:; 1’5 F3 Momsihgulw ML AMI? :23 3:3 W /W 7:11” Ill?- IDC {/0 )2—2 (0g '10—? ’5611’4‘0—‘3bfl'l’a{W} ~3019'll”’ o.(7_~lol aal o—'l_ ac, 6,), 50,104! W A'{ : 2734.15 0 C: <ETAI+EQA ; ...
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111-2006&amp;2007-1-M10-November2006_2 - gawk LINEAR...

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