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3. Consider the system of linear equations 2x₁ + 3x₂ + x3 = −1 3x₁ + 3x₂ + x3 = 1 3x₁ + 4x₂ + x3 = -2 a. Find the inverse of the coefficient matrix A. b. Using the inverse matrix of A, find the solution of the system. 4. Suppose the following matrix A is the augmented matrix for a system of linear equations A = 1 2 3 4 2 -1 -2 a² -1 -7 -11 a where a is a real number. Determine all the values of a so that the corresponding system is consistent.

3. Consider the system of linear equations 2x₁ + 3x₂ + x3 = −1 3x₁ + 3x₂ + x3 = 1 3x₁ + 4x₂ + x3 = -2 a. Find the inverse of the coefficient matrix A. b. Using the inverse matrix of A, find the solution of the system. 4. Suppose the following matrix A is the augmented matrix for a system of linear equations A = 1 2 3 4 2 -1 -2 a² -1 -7 -11 a where a is a real number. Determine all the values of a so that the corresponding system is consistent.

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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3. Consider the system of linear equations 2x₁ + 3x₂ + x3 = −1 3x₁ + 3x₂ + x3 = 1 3x₁ + 4x₂ + x3 = -2 a. Find the inverse of the coefficient matrix A. b. Using the inverse matrix of A, find the solution of the system. 4. Suppose the following matrix A is the augmented matrix for a system of linear equations A = 1 2 3 4 2 -1 -2 a² -1 -7 -11 a where a is a real number. Determine all the values of a so that the corresponding system is consistent.
Transcribed Image Text:3. Consider the system of linear equations 2x₁ + 3x₂ + x3 = −1 3x₁ + 3x₂ + x3 = 1 3x₁ + 4x₂ + x3 = -2 a. Find the inverse of the coefficient matrix A. b. Using the inverse matrix of A, find the solution of the system. 4. Suppose the following matrix A is the augmented matrix for a system of linear equations A = 1 2 3 4 2 -1 -2 a² -1 -7 -11 a where a is a real number. Determine all the values of a so that the corresponding system is consistent.
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