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The equation Ax=b is homogeneous if the zero vector is a solution. Choose the correct answer below. A. False. A system of linear equations is said to be homogeneous if it can be written in the form Ax=b, where A is an mxn matrix and b is a nonzero vector in Rm. Thus, the zero vector is never a solution of a homogeneous system. B. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax=b, where A is an mxn matrix and b is a nonzero vector in Rm. If the zero vector is a solution, then b=0. OC. False. A system of linear equations is said to be homogeneous if it can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. If the zero vector is a solution, then b=Ax=A0 = 0, which is false. D. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax=0, where A is an mxn matrix and 0 is the zero vector in Rm. If the zero vector is a solution, then b=Ax=A0 = 0.

The equation Ax=b is homogeneous if the zero vector is a solution. Choose the correct answer below. A. False. A system of linear equations is said to be homogeneous if it can be written in the form Ax=b, where A is an mxn matrix and b is a nonzero vector in Rm. Thus, the zero vector is never a solution of a homogeneous system. B. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax=b, where A is an mxn matrix and b is a nonzero vector in Rm. If the zero vector is a solution, then b=0. OC. False. A system of linear equations is said to be homogeneous if it can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in Rm. If the zero vector is a solution, then b=Ax=A0 = 0, which is false. D. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax=0, where A is an mxn matrix and 0 is the zero vector in Rm. If the zero vector is a solution, then b=Ax=A0 = 0.

Advanced Engineering Mathematics
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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d. The equation Ax = b is homogeneous if the zero vector is a solution. Choose the correct answer below. O A. False. A system of linear equations is said to be homogeneous if it can be written in the form Ax = b, where A is an m×n matrix and b is a nonzero vector in R". Thus, the zero vector is never a solution of a homogeneous system. O B. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax = b, where A is an mxn matrix and b is a nonzero vector in R". If the zero vector is a solution, then b = 0. O C. False.A system of linear equations is said to be homogeneous if it can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in R". If the zero vector is a solution, then b = Ax = A0 = 0, which is false. O D. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax = 0, where A is an mxn matrix and O is the zero vector in R". If the zero vector is a solution, thenb = Ax = A0 = 0. e. If Ax = b is consistent, then the solution set of Ax = b is obtained by translating the solution set of Ax = 0. Choose the correct answer below. O A. True. Suppose the equation Ax = b is consistent for some given b, and let p be a solution. Then the solution set of Ax = b is the set of all vectors of the form w= p+Vh, where vn is any solution of the homogeneous equation Ax = 0. O B. False. Suppose the equation Ax = b is consistent for some given b, and let p be a solution. Then the solution set of Ax = b is the set of all vectors of the form w= p+vn, where v, is any solution of the homogeneous equation Ax = 0. O C. False. Suppose the equation Ax = b is consistent for some given b. Then the solution set of Ax = b is the set of all vectors of the form w = p+vn, where vh is not a solution of the homogeneous equation Ax = 0. O D. True. Suppose the equation Ax = b is consistent for some given b. Then the solution set of Ax = b is the set of all vectors of the form w=p+vn, where v, is not a solution of the homogeneous equation Ax = 0.
Transcribed Image Text:d. The equation Ax = b is homogeneous if the zero vector is a solution. Choose the correct answer below. O A. False. A system of linear equations is said to be homogeneous if it can be written in the form Ax = b, where A is an m×n matrix and b is a nonzero vector in R". Thus, the zero vector is never a solution of a homogeneous system. O B. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax = b, where A is an mxn matrix and b is a nonzero vector in R". If the zero vector is a solution, then b = 0. O C. False.A system of linear equations is said to be homogeneous if it can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in R". If the zero vector is a solution, then b = Ax = A0 = 0, which is false. O D. True. A system of linear equations is said to be homogeneous if it can be written in the form Ax = 0, where A is an mxn matrix and O is the zero vector in R". If the zero vector is a solution, thenb = Ax = A0 = 0. e. If Ax = b is consistent, then the solution set of Ax = b is obtained by translating the solution set of Ax = 0. Choose the correct answer below. O A. True. Suppose the equation Ax = b is consistent for some given b, and let p be a solution. Then the solution set of Ax = b is the set of all vectors of the form w= p+Vh, where vn is any solution of the homogeneous equation Ax = 0. O B. False. Suppose the equation Ax = b is consistent for some given b, and let p be a solution. Then the solution set of Ax = b is the set of all vectors of the form w= p+vn, where v, is any solution of the homogeneous equation Ax = 0. O C. False. Suppose the equation Ax = b is consistent for some given b. Then the solution set of Ax = b is the set of all vectors of the form w = p+vn, where vh is not a solution of the homogeneous equation Ax = 0. O D. True. Suppose the equation Ax = b is consistent for some given b. Then the solution set of Ax = b is the set of all vectors of the form w=p+vn, where v, is not a solution of the homogeneous equation Ax = 0.
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