Guided Proof Prove that if A is row-equivalent to B , and B is row-equivalent to C , A is row-equivalent to C . Getting Started: to prove that If A is row-equivalent to C , you have to find elementary matrices E 1 , E 2 …. E k such that A = E k … E 2 E 1 C . (i) Begin by observing that A is row-equivalent to B and B is row-equivalent to C . (ii) This means that there exist elementary matrices F 1 F 2 … F n and G 1 G 2 … G m such that A = F n … F 2 F 1 B and B = G m … G 2 G 1 C . (iii) Combine the matrix equations from step (ii).
Guided Proof Prove that if A is row-equivalent to B , and B is row-equivalent to C , A is row-equivalent to C . Getting Started: to prove that If A is row-equivalent to C , you have to find elementary matrices E 1 , E 2 …. E k such that A = E k … E 2 E 1 C . (i) Begin by observing that A is row-equivalent to B and B is row-equivalent to C . (ii) This means that there exist elementary matrices F 1 F 2 … F n and G 1 G 2 … G m such that A = F n … F 2 F 1 B and B = G m … G 2 G 1 C . (iii) Combine the matrix equations from step (ii).
Solution Summary: The author explains that if A is row-equivalent to B and C are the elementary matrices.
Problem #5
Suppose you flip a two sided fair coin ("heads" or "tails") 8 total times.
a). How many ways result in 6 tails and 2 heads?
b). How many ways result in 2 tails and 6 heads?
c). Compare your answers to part (a) and (b) and explain in a few sentences why the
comparison makes sense.
A local company has a 6 person management team and 20 employees. The company needs to select 3 people from the management team and 7 employees to attend a regional meeting. How many different possibilities are there for the group that can be sent to the regional meeting?
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