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Problem 2. Consider the linear system ax₁ + bx₂ cx₁ + dx₂ = j = k, where a, b, c, d, j, k are real numbers. (a) Choose specific values of a, b, c, d for which ad-bc = 0 and show by example that you can find values of j, k for that make the system consistent and other values of j, k that make the system inconsistent. (b) Consider again the above system, but now a, b, c, d are any real numbers for which ad-bc= 0. Explain why it's always possible to find values of j,k for which the system is inconsistent.

Problem 2. Consider the linear system ax₁ + bx₂ cx₁ + dx₂ = j = k, where a, b, c, d, j, k are real numbers. (a) Choose specific values of a, b, c, d for which ad-bc = 0 and show by example that you can find values of j, k for that make the system consistent and other values of j, k that make the system inconsistent. (b) Consider again the above system, but now a, b, c, d are any real numbers for which ad-bc= 0. Explain why it's always possible to find values of j,k for which the system is inconsistent.

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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(c) Explain why the above system is always consistent with exactly one solution whenever a, b, c, d are chosen to satisfy ad-bc0.
Transcribed Image Text:(c) Explain why the above system is always consistent with exactly one solution whenever a, b, c, d are chosen to satisfy ad-bc0.
Problem 2. Consider the linear system axı + bx₂ cx₁ + dx₂ = = j k, where a, b, c, d, j, k are real numbers. (a) Choose specific values of a, b, c, d for which ad-bc = 0 and show by example that you can find values of j, k for that make the system consistent and other values of j, k that make the system inconsistent. (b) Consider again the above system, but now a, b, c, d are any real numbers for which ad bc = 0. Explain why it's always possible to find values of j,k for which the system is inconsistent.
Transcribed Image Text:Problem 2. Consider the linear system axı + bx₂ cx₁ + dx₂ = = j k, where a, b, c, d, j, k are real numbers. (a) Choose specific values of a, b, c, d for which ad-bc = 0 and show by example that you can find values of j, k for that make the system consistent and other values of j, k that make the system inconsistent. (b) Consider again the above system, but now a, b, c, d are any real numbers for which ad bc = 0. Explain why it's always possible to find values of j,k for which the system is inconsistent.
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