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Let A E Rmxn and be Rm. Consider the following statements: (a) The system Az = b has a solution (b) There exists y such that yA = 0, y¹b ‡ 0. (1) Show that both (a) and (b) do not hold simultaneously. (2) Assuming that (a) is not true, show that (b) holds.

Let A E Rmxn and be Rm. Consider the following statements: (a) The system Az = b has a solution (b) There exists y such that yA = 0, y¹b ‡ 0. (1) Show that both (a) and (b) do not hold simultaneously. (2) Assuming that (a) is not true, show that (b) holds.

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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matrix analysis practice question,Please write the simplest answer process,thanks
Let A E Rmxn and be Rm. Consider the following statements: (a) The system Az = b has a solution (b) There exists y such that yA = 0, y¹b ‡ 0. (1) Show that both (a) and (b) do not hold simultaneously. (2) Assuming that (a) is not true, show that (b) holds.
Transcribed Image Text:Let A E Rmxn and be Rm. Consider the following statements: (a) The system Az = b has a solution (b) There exists y such that yA = 0, y¹b ‡ 0. (1) Show that both (a) and (b) do not hold simultaneously. (2) Assuming that (a) is not true, show that (b) holds.
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