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Math 205A Exam I, page 1 October 5, 2007 FIRST NAME. bed 7 | 2a 013 Of 4c 1. Suppose the augmented matrix of the matrix equation Ax=bis: | 0 0 0 3] 69 00 0 —5| & 00 0 Of 10p 1A. This augmented matrix is not quite in reduced row echelon form. Find the reduced row echelon form; circh i matri: form; circle your final matrix. hig on podF da donc) 2a. | ji or FO} Ge eae hq 10 4 O [Za -IMg 0 0 0 316% oe ooo! | 29 o ee as 00-5) 8K | 387s fo Se ele oe eee ed: BK Cee eae eee P 4454, ot, fe ° 8@ @ 6 Hp Te : 6: SMe disled (0 4 by-S bist = dccopteal ai J te Tiel: ee rages Aaah Crréaven . However, if Gind prreserteck here ; usa GK 4/05 £0, tek cal. ste Ba ep heey) Pas ee at [8] clr paites| 1B. Use the answer to (1A) to answer these questions: What conditions are there on a, c, g, k and p so that Ax = b has... 1B-i. ...NO solutions. (tell me about all of a, ¢, g, & and p in each of these three parts). If BKrley ZO OR op AO [ow bok" 5 omlettel] aEiK CER Dhecice Shoilac Aressee if fre ave ifia canakinke in & Ufrict arn, BMS orte pre aquvelnt o- 1B-ii. ...exactly one solution. - Cant. bnypen- the onitence 4 2 tra nile rls Ht thee ave Omang Sant if he ewrsisleney 9 ond Pons ofoame, 1B-iii. ... infinitely many solutions. f K+ =O AWD lp =O, ak, CER 1C: Suppose that a,c, g, k and p are in fact chosen so that Ax = b is consistent. Give the particular solution obtained by setting any and all free variables equal to 2; your answer will be in terms of a, ¢, g, Kk and p. op Lips Xo aan -4x, X= 2a- lg -8 ) hae cahl ‘ = is . = =4c-6 9 aging he He > Sy sl x22 yi oe woogie X= free. ee hurler 4 24 A gris if X= 24 ape reduchies 8 
