4. [lesj Suppose you are given the set A={u = (0,1,2), v = (-1,0,0)}. Describe how you would combine A with a suitable vector from the set B = {z =(-5,2,4), w = (0, 2, 2), s = (3,3,6)} to obtain a generating set for R³. Your answer should contain the following (according to order): • the proof that u and v are linearly independent • the reason why A cannot generate R³ by itself the proof that any vector (x, y,z) eR' can be written as a linear combination of AU{your chosen vector from B} (i.e. {u, v, z} or {u, v, w} or {u, v, s}) Hint: Use my instruction in question 3 as a guide. • the argument of whether either one of the two remaining vectors of B that you did not choose might work as well or might not work at all (i.e. give reasons for your claim)

4. [lesj Suppose you are given the set A={u = (0,1,2), v = (-1,0,0)}. Describe how you would combine A with a suitable vector from the set B = {z =(-5,2,4), w = (0, 2, 2), s = (3,3,6)} to obtain a generating set for R³. Your answer should contain the following (according to order): • the proof that u and v are linearly independent • the reason why A cannot generate R³ by itself the proof that any vector (x, y,z) eR' can be written as a linear combination of AU{your chosen vector from B} (i.e. {u, v, z} or {u, v, w} or {u, v, s}) Hint: Use my instruction in question 3 as a guide. • the argument of whether either one of the two remaining vectors of B that you did not choose might work as well or might not work at all (i.e. give reasons for your claim)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

4. [ e Suppose you are given the set A={u=(0,1,2), v = (-1,0,0)}.
Describe how you would combine A with a suitable vector from the set
B= {z=(-5,2,4),w=(0,2,2), s =(3,3,6)} to obtain a generating set for R'.
Your answer should contain the following (according to order):
• the proof that u and v are linearly independent
• the reason why A cannot generate R³ by itself
the proof that any vector (x, y,z) eR' can be written as a linear combination of
AU{your chosen vector from B} (i.e. {u, v, z} or {u, v, w} or {u, v, s})
Hint: Use my instruction in question 3 as a guide.
• the argument of whether either one of the two remaining vectors of B that you did not
choose might work as well or might not work at all (i.e. give reasons for your claim)

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