Unformatted text preview: Chapter 1 ISM: Linear Algebra b. Proceeding as in part {a}, we ﬁnd (3,1,!) = [—%t,t]. 1:. Proceedings as in part {a}, we ﬁnd only the solution [[1, ll}. 24. Let 'u be the speed of the boat relative to the water, and s be the speed of the stream;
then the speed of the boat relative to the land is U + a downstream and o — s upstream. Using the tact that [distance] 2 [speed}{time}, we obtain the system 8 = 'l‘” ‘l‘ Sli <— downstream
3 = (t; _ 3}% <— upstream
The solution is 1: =18 and s = 6.
3+2 :1
25. The system reduces to y — 2.2 = —3
I] = I: — ’F a. The system has solutions ifk — 'i' = G, or k = T.
b. If I: = 7 then the system has inﬁnitely many solutions. :3. If I: = 7 then we can choose 2 = t freely and obtain the solutions {1:11:12} ={1— tj—3+2t,t]. 
,_. 5—32
y—l—ﬂz
{152—4}; 2 k—E 
,_. 26. The system reduces to This system has a unique solution if k2 — 4 7E D, that is, if I: 3E ii.
If J: = 2, then the last equation is [l = ﬂ, and there will be inﬁnitely many solutions. If k = —2, then the last equation is I] = —4, and there will be no solutions.
2'17. Let I = the number of male children and y = the number of female children. Then the statement “Emile has twice as many sisters as brothers” translates into 1.! = 2E2: — 1] and “Gertrude has as many brothers as sisters” translates into I=y—1. ...
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 Spring '09
 Derksen
 Algebra

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