Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a', then specify a value or comma-separated list of values. 3x1+6x2-3x3 = -12 3x1+6x₂+2x3 = -2 ax1+2x2-4x3 = -10 No Solutions: Always Unique Solution: Never Infinitely Many Solutions: Never Comments: You have indicated that the system always has no solution. However, there is no value of a for which the system has no solution. You have indicated that the system never has a unique solution. However, the system has a unique solution whenever a 1. You have indicated that the system never has infinitely many solutions. However the system has infinitely many solutions when a = 1
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a', then specify a value or comma-separated list of values. 3x1+6x2-3x3 = -12 3x1+6x₂+2x3 = -2 ax1+2x2-4x3 = -10 No Solutions: Always Unique Solution: Never Infinitely Many Solutions: Never Comments: You have indicated that the system always has no solution. However, there is no value of a for which the system has no solution. You have indicated that the system never has a unique solution. However, the system has a unique solution whenever a 1. You have indicated that the system never has infinitely many solutions. However the system has infinitely many solutions when a = 1
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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step by step of making REF to get the value of a
Transcribed Image Text:Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a= ', or 'a #', then specify a
value or comma-separated list of values.
3x1+6x2-3x3 = -12
3x1+6x₂+2x3 = -2
ax1+2x₂-4x3 = -10
No Solutions:
Always
Unique Solution:
Never
Infinitely Many Solutions: Never
Comments:
You have indicated that the system always has no solution. However, there is no value of a for which the system has no solution.
You have indicated that the system never has a unique solution. However, the system has a unique solution whenever a 1.
You have indicated that the system never has infinitely many solutions. However, the system has infinitely many solutions when a = 1.
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