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 fand g are arbitrary, c and d can be any value and the system will be consistent. OB. 11 +][ to C d g 0 d-11c g-cf arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an equation of bx₂=0 where b is nonzero. Thus, c=d=0. The row reduction of O D. 1 11 The row reduction of FIX 1 1 11 f OC. 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 f X₁ + 11x₂=f Cx₁ + x₂=g shows that d-11c=0 since f and g are 1 11 f shows that d-11c #0 since f and g are arbitrary с dg 0 d-11c g-cf Otherwise, for some choices off and g, the second row could correspond to an equation of 0=b, where b is nonzero. Thus, d# 11c.
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 fand g are arbitrary, c and d can be any value and the system will be consistent. OB. 11 +][ to C d g 0 d-11c g-cf arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an equation of bx₂=0 where b is nonzero. Thus, c=d=0. The row reduction of O D. 1 11 The row reduction of FIX 1 1 11 f OC. 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 f X₁ + 11x₂=f Cx₁ + x₂=g shows that d-11c=0 since f and g are 1 11 f shows that d-11c #0 since f and g are arbitrary с dg 0 d-11c g-cf Otherwise, for some choices off and g, the second row could correspond to an equation of 0=b, where b is nonzero. Thus, d# 11c.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.
O A. Since f and g are arbitrary, c and d can be any value and the system will be consistent.
O B.
O D.
yamnle
The row reduction of
1 11
[
C dg
arbitrary. Otherwise, for some choices of f and g, the second row could correspond to an equation of
bx₂=0 where b is nonzero. Thus, c=d=0.
The row reduction of
to
Taythank
HITS
1 11 f
OC. 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.
1
11
0 d-11c g-cf
to
f
1
[
shows that d-11c #0 since f and g are arbitrary
C dg
Otherwise, for some choices off and g, the second row could correspond to an equation of 0=b, where b
is nonzero. Thus, d# 11c.
X₁ + 11x₂=f
CX₁ + dx₂=g
shows that d-11c=0 since f and
g are
11
f
0 d-11c g-cf
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