Find a basis for the solution space of the difference equation. Prove that the solutions found span the solution set. Yk+29Yk+1+14yk = 0 Find a basis for the solution space of the difference equation. Choose the correct answer below. OA. 9k, 14k C. 2k E. 7k O G. 2,7k, 14k Prove that the solutions found span the solution set. Choose the correct answer below. OB. 14k O D. 2,7 OF. 0,2,7,14 OH. 2,7k O A. Since the solutions are linearly independent and satisfy the homogeneous linear difference equation, the solutions automatically span the solution space. B. Since the difference equation is homogeneous and of order 3, the set of all solutions is a 3-dimensional vector space. Since the basis and the solution set have the same dimension, the solutions span the solution set. C. Since the difference equation is homogeneous and of order 2, the set of all solutions is a 2-dimensional vector space. Since the basis and the solution set have the same dimension, the solutions span the solution set. O D. Since the difference equation is homogeneous and of order 2, the set of all solutions is a 2-dimensional vector space. Since any linear combination of solutions is also a solution, the solutions span the solution space.
Find a basis for the solution space of the difference equation. Prove that the solutions found span the solution set. Yk+29Yk+1+14yk = 0 Find a basis for the solution space of the difference equation. Choose the correct answer below. OA. 9k, 14k C. 2k E. 7k O G. 2,7k, 14k Prove that the solutions found span the solution set. Choose the correct answer below. OB. 14k O D. 2,7 OF. 0,2,7,14 OH. 2,7k O A. Since the solutions are linearly independent and satisfy the homogeneous linear difference equation, the solutions automatically span the solution space. B. Since the difference equation is homogeneous and of order 3, the set of all solutions is a 3-dimensional vector space. Since the basis and the solution set have the same dimension, the solutions span the solution set. C. Since the difference equation is homogeneous and of order 2, the set of all solutions is a 2-dimensional vector space. Since the basis and the solution set have the same dimension, the solutions span the solution set. O D. Since the difference equation is homogeneous and of order 2, the set of all solutions is a 2-dimensional vector space. Since any linear combination of solutions is also a solution, the solutions span the solution space.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Find a basis for the solution space of the difference equation. Prove that the solutions found span the solution set.
Yk+29Yk+1+14yk = 0
Find a basis for the solution space of the difference equation. Choose the correct answer below.
OA. 9k, 14k
OC. 2k
OE. 7k
G. 2,7k, 14k
Prove that the solutions found span the solution set. Choose the correct answer below.
B. 14k
D. 2,7
OF. 0,2,7,14
OH. 2k,7k
O A. Since the solutions are linearly independent and satisfy the homogeneous linear difference equation, the solutions automatically span the solution space.
B. Since the difference equation is homogeneous and of order 3, the set of all solutions is a 3-dimensional vector space. Since the basis and the solution set have the same dimension, the
solutions span the solution set.
C. Since the difference equation is homogeneous and of order 2, the set of all solutions is a 2-dimensional vector space. Since the basis and the solution set have the same dimension, the
solutions span the solution set.
D. Since the difference equation is homogeneous and of order 2, the set of all solutions is a 2-dimensional vector space. Since any linear combination of solutions is also a solution, the
solutions span the solution space.
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