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Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is homogeneous if the zero vector is a solution. Choose the correct answer below. O A. The statement is 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. O B. The statement is 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. O C. The statement is 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. OD. The statement is 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.

Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is homogeneous if the zero vector is a solution. Choose the correct answer below. O A. The statement is 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. O B. The statement is 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. O C. The statement is 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. OD. The statement is 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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Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is homogeneous if the zero vector is a solution. Choose the correct answer below. O A. The statement is 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. O B. The statement is 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. O C. The statement is 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. OD. The statement is 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.
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is homogeneous if the zero vector is a solution. Choose the correct answer below. O A. The statement is 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. O B. The statement is 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. O C. The statement is 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. OD. The statement is 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.
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