Let be given the following linear system x + 2y – 3z = 4 3.x – y+ 5z = 2 4.x + y + (a? – 14)z = a + 2 where a E R is a parameter. 1-Determine the augmented matrix A associated to linear system (1) and give a row-echelon form. 2- Determine the value of the parameter a E R for which the system (1) has: a- no solution b- exactly one solution c- infinitely many d- solve the system (1) in the case of infinitely many solutions. solutions 0.

Algebra and Trigonometry (MindTap Course List)
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Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter11: Matrices And Determinants
Section11.CR: Chapter Review
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Let be given the following linear system
x + 2y – 3z = 4
3.x – y+ 5z = 2
4.x + y + (a? – 14)z = a + 2
where a E R is a parameter.
1-Determine the augmented matrix A associated to linear system (1) and give a row-echelon form.
2- Determine the value of the parameter a E R for which the system (1) has:
a- no solution
b- exactly one solution
c- infinitely many
d- solve the system (1) in the case of infinitely many solutions.
solutions
0.
Transcribed Image Text:Let be given the following linear system x + 2y – 3z = 4 3.x – y+ 5z = 2 4.x + y + (a? – 14)z = a + 2 where a E R is a parameter. 1-Determine the augmented matrix A associated to linear system (1) and give a row-echelon form. 2- Determine the value of the parameter a E R for which the system (1) has: a- no solution b- exactly one solution c- infinitely many d- solve the system (1) in the case of infinitely many solutions. solutions 0.
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