then put the augmented matrix into reduced row echelon form 1 1 500 1 2 1000

Then put the augmented matrix into reduced row

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2. Use linear equations to find a polynomialp(x) withp(0) = 1,p(1) = 0,p(2) = 5,p(3) = 22. 3. Consider the following network of irrigation channels with flows mea-sured in, say, thousands of litres per day. B x 2 @ @ @ @ @ @ @ x 5 10 / A x 1 ? x 3 @ @ @ @ @ @ @ @ D 7 / C 3 x 4 ? ~ ~ ~ ~ ~ ~ ~ ~ 7
(a) Set up and solve a linear system for the possible flowsx1, x2, x3, x4, x5,usingx4andx5as free variables.(b) Can we close both channels BC and CD?(c) Find the maximum and minimum possible flowx4through channelCD. Solution: 4. Consider the following road network with traffic flows measured in,say, hundreds of cars per hour. A x 1 x 2 @ @ @ @ @ @ @ @ B 8 o x 3 C 3 ~ ~ ~ ~ ~ ~ ~ 3 ? ? ? ? ? ? ? ? D x 5 / E x 4 O 8
(a) Set up and solve a linear system for the possible flowsx1, x2, x3, x4, x5.(b) Find the maximum and minimum possible traffic flow for each roadAD, AC, BC, EB, and DE.(c) Is it possible to close two of these five roads at once? Solution:

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