Suppose the system to the right is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer. Select the correct answer below. O A. Since f and g are arbitrary, c and d can be any value and the system will be consistent. OB. O C. The row reduction of to 1 13 f 1 13 f с с dg 0 d 13c g-cf equation of 0 =b, where b is nonzero. Thus, d# 13c. H to equation of bx₂=0 where b is nonzero. Thus, c= d = 0. O D. Since f and g are arbitrary and the system is consistent for all possible values of f and g, c = 0 and d = 1. Otherwise, the triangular form of the matrix will show that the system is inconsistent. The row reduction of 1 13 f c d g …... 13 f 0 d 13c g-cf X₁ + 13x₂=f CX₁ + dx₂ = g shows that d - 13c #0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an shows that d - 13c=0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an

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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Question
Suppose the system to the right is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer.
Select the correct answer below.
A. Since f and g are arbitrary, c and d can be any value and the system will be consistent.
B.
1
f
13
0 d 13c g- cf
с
g
equation of 0 =b, where b is nonzero. Thus, d # 13c.
C.
The row reduction of
1 13
The row reduction of
1 13 f
1
13
f
[:]
g
0 d-13c g- cf
equation of bx₂=0 where b is nonzero. Thus, c = d=0.
D. Since f and g are arbitrary and the system is consistent for all possible values of f and g, c = 0 and d = 1. Otherwise, the triangular form of the matrix will show that the system is inconsistent.
to
с d
X₁ + 13x₂ = f
CX₁ + dx₂ = g
to
shows that d - 13c #0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an
shows that d - 13c=0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an
Transcribed Image Text:Suppose the system to the right is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer. Select the correct answer below. A. Since f and g are arbitrary, c and d can be any value and the system will be consistent. B. 1 f 13 0 d 13c g- cf с g equation of 0 =b, where b is nonzero. Thus, d # 13c. C. The row reduction of 1 13 The row reduction of 1 13 f 1 13 f [:] g 0 d-13c g- cf equation of bx₂=0 where b is nonzero. Thus, c = d=0. D. Since f and g are arbitrary and the system is consistent for all possible values of f and g, c = 0 and d = 1. Otherwise, the triangular form of the matrix will show that the system is inconsistent. to с d X₁ + 13x₂ = f CX₁ + dx₂ = g to shows that d - 13c #0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an shows that d - 13c=0 since f and g are arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an
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