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e Math 205 A B Quiz 05 blue page 1 10/26/2012 Name__Sv4qorted soln 1, The consumption matrix C for an economy with three sectors G, H and M and the final demand vector d of the open 0.02 0.1 0.01 400 sector areC = | 0.01 0.2 0.05 | andd= | 500 |, respectively. 0.03 0.4 0.07 600 1A) Find x, the vector showing the total numbers of units of goods produced by the three sectors G, H and M. Show all your work and your answer rounded to TWO digits after the decimal point. Wwe Know theA X=CK+A o, (£,-c)x =a Phan one ot. looot te » p veceed' @ fink eee fey -c|z]) @ fink X= (,-c)1H citer nelod procloces a x=} 6 90,99 OM ont 4 ay “yes GSBul “| per vare d H madd 1B) Each unit produced by H requires how many units of G’s product? CD 640.99 unt H mde) = 1C) Of the total number of units produced by M, how many are consumed by H? “os. -sS 0.4 % 690.99 unik 4M 296.4? united M1 21 3 41 a ( Pe Anew hy 10 2 2LetC=| 4 3 5 6 7/|,thentheRREFofCis|0 1 -1 -2 0 ptt “uf E -1 -15 -22 3 [: a) ny fon Label the columns of Cas ¢1, €2, «--- 95 G12 / ) 2A) Find a basis for Col(C). Don’t write the vectors out; use the names c), etc. . : Ss a The RREF 4 C tlk ox the pret cokimas of C fon & nes oo fc, 92 sf 2B) Find the sum s of the last three column vectors of C. Now, s must be in Col(C). Indeed, express s as a LC of the basis vectors from part 2A. Show any matrices (augmented, RREF’d, etc) involved in your work. vy het Hree. > a f 3444 8 re: ib ye ark & S=Ceh ete _ Nore: ay” Gt gtr vot |= cds. RREF C yoo -15 -21 414 7 yt [3] Hi & Nor 2, ! 2 > Bae ib Us SK, 3K, + ke Vane the Kis ave teas. J Rh C) Know WHY Hheoe vei On the Game in “free to LCs} 
