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Answer all questions. Given c= [C₁] C₂ C3 , where C1, C2, C3, C4 is 1, 2, 3, 4 respectively. (a) Obtain a coefficient matrix A with non-zero entries such that the system of four equations in four unknowns represented by Ax = b has an infinite number of solutions with one free variable, with x = c as one of the solutions. Verify your answer. (b) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system has the unique solution x = c. Verify your answer. (c) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system is inconsistent. Verify your answer.

Answer all questions. Given c= [C₁] C₂ C3 , where C1, C2, C3, C4 is 1, 2, 3, 4 respectively. (a) Obtain a coefficient matrix A with non-zero entries such that the system of four equations in four unknowns represented by Ax = b has an infinite number of solutions with one free variable, with x = c as one of the solutions. Verify your answer. (b) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system has the unique solution x = c. Verify your answer. (c) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system is inconsistent. Verify your answer.

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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Answer all questions. Given c= [C₁ C₂ C3 where C1, C2, C3, C4 is 1, 2, 3, 4 respectively. (a) Obtain a coefficient matrix A with non-zero entries such that the system of four equations in four unknowns represented by Ax = b has an infinite number of solutions with one free variable, with x = c as one of the solutions. Verify your answer. (b) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system has the unique solution x = c. Verify your answer. (c) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system is inconsistent. Verify your answer.
Transcribed Image Text:Answer all questions. Given c= [C₁ C₂ C3 where C1, C2, C3, C4 is 1, 2, 3, 4 respectively. (a) Obtain a coefficient matrix A with non-zero entries such that the system of four equations in four unknowns represented by Ax = b has an infinite number of solutions with one free variable, with x = c as one of the solutions. Verify your answer. (b) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system has the unique solution x = c. Verify your answer. (c) Add a fifth equation with non-zero coefficients to your system in (a) such that the new system is inconsistent. Verify your answer.
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