d Oliver starts with a collection of bricks in which the combined of blue and green bricks is odd. Explain why he cannot end up with a combined number of blue and green bricks that is even.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
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Chapter6: Systems Of Equations And Inequalities
Section6.1: Linear And Nonlinear Systems Of Equations
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Oliver got frustrated sometimes with his somewhat limited set of red
blue, and green building bricks. Part way through a project, he often ran
out of bricks of one particular colour. So he invented some 3D printing
machines that transform a brick of one colour into a combination of
bricks of one or more colours. Each machine can also operate in reverse
The red machine (R) converts 1 red brick (r) into 1 blue brick (b) and 1
green brick (g). This process and its reverse are represented by
R-1
+ r.
R
bg and bg
Similarly, for the blue machine (B) we have
B
B-1
b 2 rg
and rg
+b.
And for the green machine (G) we have
G rb and rb
G-
g.
g
The machines can be used on collections of bricks, performing one con-
version at a time. For example, 3 blue bricks can be converted into 1
red and 3 green bricks in three steps, as follows:
B
bbb
→ rgbb
В
G-
→ rgrgb
→ rggg
Note that the order of the bricks in each collection is irrelevant.
Transcribed Image Text:Oliver got frustrated sometimes with his somewhat limited set of red blue, and green building bricks. Part way through a project, he often ran out of bricks of one particular colour. So he invented some 3D printing machines that transform a brick of one colour into a combination of bricks of one or more colours. Each machine can also operate in reverse The red machine (R) converts 1 red brick (r) into 1 blue brick (b) and 1 green brick (g). This process and its reverse are represented by R-1 + r. R bg and bg Similarly, for the blue machine (B) we have B B-1 b 2 rg and rg +b. And for the green machine (G) we have G rb and rb G- g. g The machines can be used on collections of bricks, performing one con- version at a time. For example, 3 blue bricks can be converted into 1 red and 3 green bricks in three steps, as follows: B bbb → rgbb В G- → rgrgb → rggg Note that the order of the bricks in each collection is irrelevant.
d Oliver starts with a collection of bricks in which the combined number
of blue and green bricks is odd. Explain why he cannot end up with
a combined number of blue and green bricks that is even.
Transcribed Image Text:d Oliver starts with a collection of bricks in which the combined number of blue and green bricks is odd. Explain why he cannot end up with a combined number of blue and green bricks that is even.
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