Math 205 A B Quiz 05 blue page 1 10/26/2012 Name
1. The consumption matrix Cfor an economy with three sectors G,Hand Mand the final demand vector dof the open
sector are C=
0.02 0.1 0.01
0.01 0.2 0.05
0.03 0.4 0.07
and d=
400
500
600
, respectively.
1A) Find x, the vector showing the total numbers of units of goods produced by the three sectors G,Hand M. Show all
your work and your answer rounded to TWO digits after the decimal point.
1B) Each unit produced by Hrequires how many units of G’s product?
1C) Of the total number of units produced by M, how many are consumed by H?
2. Let C=
2 1 3 4 1
4 3 5 6 7
−8−1−15 −22 14
, then the RREF of Cis
1 0 2 3 0
0 1 −1−2 0
0 0 0 0 1
.
Label the columns of Cas c1,c2, . . . .
2A) Find a basis for Col(C). Don’t write the vectors out; use the names c1, etc.
2B) Find the sum sof the last three column vectors of C. Now, smust be in Col(C). Indeed, express sas a LC of the
basis vectors from part 2A. Show any matrices (augmented, RREF’d, etc) involved in your work.