termine the values of a for which the system nas no solutions, exactly one solution, or x + 2y – 3z = 5 2x – y + 2z = 3 :+ 5y + (a² – 16)z = a + 15 %3D -a = i there is no solution. - a = i there are infinitely many solutions. -a+± i the system has exactly one solution.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions.
x + 2y – 3z = 5
2x – y + 2z = 3
5x + 5y + (a? – 16)z = a + 15
For a =
i
there is no solution.
For a =
i
there are infinitely many solutions.
For a +±
i
the system has exactly one solution.
Transcribed Image Text:Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y – 3z = 5 2x – y + 2z = 3 5x + 5y + (a? – 16)z = a + 15 For a = i there is no solution. For a = i there are infinitely many solutions. For a +± i the system has exactly one solution.
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