Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Chapter 2.4, Problem 8P
Explanation of Solution
Argument showing that the collection must be linearly dependent:
- If we take a collection of three or more
vectors in two-dimensional space and make a matrix from the vector as rows, then the matrix will have 2 columns and three or more rows. - Then the rank of matrix will be always 2...
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Prove that in a given vector space V, the zero vector is unique.
Suppose, by way of contradiction, that there are two distinct additive identities 0 and u,. Which of the following statements are then true about the vectors 0 and u,? (Select all that apply.)
O The vector 0 + u, is not equal to u, + 0.
O The vector 0 + u, is equal to un:
O The vector 0 + u, is not equal to 0.
O The vector 0 + u, does not exist in the vector space V.
O The vector 0 + u, is equal to 0.
O The vector o + u, is not equal to u:
Which of the following is a result of the true statements that were chosen and what contradiction then occurs?
O The statement u, + o 0, which contradicts that u, is an additive identity.
O The statement u, +0 # 0 + u, which contradicts the commutative property.
O The statement u, = 0, which contradicts that there are two distinct additive identities.
O The statement u, + 0 U, which contradicts that O is an additive identity.
O The statement u, + 0 + 0, which contradicts that u, must…
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))
CY
ve haber
Share
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
Chapter 2 Solutions
Introduction to mathematical programming
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
Knowledge Booster
Similar questions
- 8. Determine whether the set W = {(a1,a2) E R²| 3a1 - 5az = 12} is a subspace of the vector space R. %3! of the vector space R.arrow_forward2. 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?arrow_forwardA 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 OU is a vector space with basis {(0, 0, 1), (0, 1,0). (1,0,0)) U = {(x, y, z) : x - y - z = 0 (mod 2)}arrow_forward
- Is W a subspace of the vector space? If not, state why. (Select all that apply.) w is the set of all vectors in R° whose components are Pythagorean triples. (Assume all components of a Pythagorean triple are positive integers.) O w is a subspace of R°. O w is not a subspace of R because it is not closed under addition. O w is not a subspace of R³ because it is not closed under scalar multiplication.arrow_forwardWrite a program that can inverse a matrix by using an approach to find its minor, cofactor and adjugate matrix. Test your program with the given matrix ?arrow_forward3) Show that the set of three-dimensional coordinates {(x, y, z)|x, y, z E Z} has size equal to N.arrow_forward
- 4. Consider the set V of vectors (x, X2, X3, X4) ER such that X1 + x3 = 0 and x, + x4 = 0. a) Prove that V is a subspace of R*. b) Give a basis and the dimension of V.arrow_forwarduse my ID : 201909010 SOLVE ALL BY matlab Consider the graphs of the functions f(x) = m - 1x and g(x) = 2x² — n where m and n are the maximum and mean values of the digits in your student-ID number. a) Create a vector v whose elements are the digits of your student-ID number. b) Create a variable m and assign the maximum digit in v to it. Create a variable n and assign the mean value of the digits in v to it. d) Define the function f(x) and g(x) above as anonymous functions. Plot the graphs of f(x) and g(x) on the same figure using the MATLAB function ezplot. f) Find the exact values of the x-coordinates of the intersection points between the two graphs using the MATLAB function solve. g) Find the area bounded by the two graphs.arrow_forwardGiven A = {1,2,3} and B={u,v}, determine. a. A X B b. B X Barrow_forward
- Write a program that can inverse a matrix by using an approach to find its minor, cofactor and adjugate matrix. Test your program with the given matrix ? Please provide in Python programarrow_forwardUSING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don’t need to be modified or added. Please show steps and explain.arrow_forwardLet H = : 8x² + 8y² s which represents the set of points on and inside an circle in the xy-plane. Find two specific examples-two vectors, and a vector and a scalar-to show that H is not a subspace of R2 H is not a subspace of R2 because the two vectors show that H V closed under (Use a comma to separate vectors as needed.) Clear all Check answer Help me solve this View an example Get more help -arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole