Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 2, Problem 13RP
Explanation of Solution
Determining the dependency of the given sets of
Consider the given sets of vectors,
A matrix A is formed as given below; whose rows are the above given vectors:
The Gauss-Jordan method is applied to find the dependency of the above given sets of vectors.
Replace row 2 by (row 2 – 2 (row 1)), then the following matrix is obtained,
Now, replace row 2 by (
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Let V₁
a)
show that none of vectors V₁, V₂, and V3 can be written as a linear AME
combination of the other two, i.e., show that the only linear combination which gives
the zero vector ₁V₁ C₂V₂ + C3V3 = 0 is where, C₁ C2 C3 = 0.
b)) show that each of vectors V₁, V2, V3, and V can be written as a linear
combination of the other three, i.e., find the constants c₁, c2 and c3 in the linear
combination G₂ V₁ + G₂V₂ + 3V3 = V₁ such that not all c, are zeros.
V4
2. For a n-vector x, and
X1 + x2
X2 + x3
y = Ax =
Xn-1 + Xn
a) Find A
b) Are the columns of A linearly independent? Justify your answer?
c) Are the rows of A linearly independent? Justify your answer?
m
U=((x,y.2) : x-y-z = 0 (mod 2)}
A collection of 3-vectors, U, is defined over Z₂ by the condition
Which of the following statements holds true of ?
O (1,1,1) EU
OU is not a vector space since it does not satisfy closure under scalar multiplication.
OU is not a vector space since it is not closed under vector addition.
O (1,0,1) U
O U is a vector space with basis {(0, 0, 1), (0, 1,0). (1,0,0))
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Chapter 2 Solutions
Operations Research : Applications and Algorithms
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - Prob. 7PCh. 2.2 - Prob. 1PCh. 2.3 - Prob. 1PCh. 2.3 - Prob. 2P
Ch. 2.3 - Prob. 3PCh. 2.3 - Prob. 4PCh. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Prob. 9PCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.6 - Prob. 1PCh. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Prob. 4PCh. 2 - Prob. 1RPCh. 2 - Prob. 2RPCh. 2 - Prob. 3RPCh. 2 - Prob. 4RPCh. 2 - Prob. 5RPCh. 2 - Prob. 6RPCh. 2 - Prob. 7RPCh. 2 - Prob. 8RPCh. 2 - Prob. 9RPCh. 2 - Prob. 10RPCh. 2 - Prob. 11RPCh. 2 - Prob. 12RPCh. 2 - Prob. 13RPCh. 2 - Prob. 14RPCh. 2 - Prob. 15RPCh. 2 - Prob. 16RPCh. 2 - Prob. 17RPCh. 2 - Prob. 18RPCh. 2 - Prob. 19RPCh. 2 - Prob. 20RPCh. 2 - Prob. 21RPCh. 2 - Prob. 22RP
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Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
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