Mark each statement True or False. Justify each answer. a. A homogeneous system of equations can be inconsistent. Choose the correct answer below. O A. False. A homogeneous equation can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 always has at least one solution, namely x = 0. Thus, a homogeneous system of equations cannot be inconsistent. OB. True. A homogeneous equation can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 always has at least one solution, namely x = 0. Thus, a homogeneous system of equations can be inconsistent. O C. False. A homogeneous equation cannot be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 does not have the solution x = 0. Thus, a homogeneous system of equations cannot be inconsistent. O D. True. A homogeneous equation cannot be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 does not have the solution x = 0. Thus, a homogeneous system of equations can be inconsistent. b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below.
Mark each statement True or False. Justify each answer. a. A homogeneous system of equations can be inconsistent. Choose the correct answer below. O A. False. A homogeneous equation can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 always has at least one solution, namely x = 0. Thus, a homogeneous system of equations cannot be inconsistent. OB. True. A homogeneous equation can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 always has at least one solution, namely x = 0. Thus, a homogeneous system of equations can be inconsistent. O C. False. A homogeneous equation cannot be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 does not have the solution x = 0. Thus, a homogeneous system of equations cannot be inconsistent. O D. True. A homogeneous equation cannot be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. Such a system Ax = 0 does not have the solution x = 0. Thus, a homogeneous system of equations can be inconsistent. b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below.
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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Transcribed Image Text:Mark each statement True or False. Justify each answer.
a. A homogeneous system of equations can be inconsistent. Choose the correct answer below.
O A. False. A homogeneous equation can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero
vector in R". Such a system Ax = 0 always has at least one solution, namely x = 0. Thus, a homogeneous system of
equations cannot be inconsistent.
B. True. A homogeneous equation can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector
in RM. Such a system Ax = 0 always has at least one solution, namely x = 0. Thus, a homogeneous system of
equations can be inconsistent.
OC. False. A homogeneous equation cannot be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero
vector in R". Such a system Ax = 0 does not have the solution x = 0. Thus, a homogeneous system of equations
cannot be inconsistent.
O D. True. A homogeneous equation cannot be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero
vector in R". Such a system Ax = 0 does not have the solution x= 0. Thus, a homogeneous system of equations
can be inconsistent.
b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below.
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