Suppose Ax = b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the trivial solution. Choose the correct answer. O A. Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution. O B. Since Ax =b is inconsistent, then the solution set of Ax = 0 is also inconsistent. The solution set of Ax = 0 is inconsistent if and only if Ax = 0 has only the trivial solution. O C. Since Ax = b is inconsistent, its solution set is obtained by translating the solution set of Ax = 0. For Ax =b to be inconsistent, Ax 0 has only the trivial solution.
Suppose Ax = b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the trivial solution. Choose the correct answer. O A. Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution. O B. Since Ax =b is inconsistent, then the solution set of Ax = 0 is also inconsistent. The solution set of Ax = 0 is inconsistent if and only if Ax = 0 has only the trivial solution. O C. Since Ax = b is inconsistent, its solution set is obtained by translating the solution set of Ax = 0. For Ax =b to be inconsistent, Ax 0 has only the trivial solution.
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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Transcribed Image Text:Suppose Ax = b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the trivial solution.
Choose the correct answer.
O A. Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the
solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution.
O B. Since Ax =b is inconsistent, then the solution set of Ax = 0 is also inconsistent. The solution set of Ax = 0 is inconsistent if and only if Ax = 0 has only the
trivial solution.
O C. Since Ax = b is inconsistent, its solution set is obtained by translating the solution set of Ax = 0. For Ax =b to be inconsistent, Ax 0 has only the trivial
solution.
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