1) Consider the following linear system: x + 2y + 4z = 2 -2x-3y -6 z= -1 x+2y+d²z =d For what values of d does this system have: (i) no solutions; (ii) exactly one solution; (iii) infinitely many solutions?
1) Consider the following linear system: x + 2y + 4z = 2 -2x-3y -6 z= -1 x+2y+d²z =d For what values of d does this system have: (i) no solutions; (ii) exactly one solution; (iii) infinitely many solutions?
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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![1) Consider the following linear system:
x+2y + 4z = 2
-2x −3 y −6 z= −1
-
x +2y+dz =d
For what values of d does this system have: (i) no solutions; (ii) exactly one
solution; (iii) infinitely many solutions?
[Hints: If you are going to divide by an expression, make certain that it is not
equal to zero. Also, if you come across a term that is the difference of two
squares, consider factoring it. In each case, list all values of d.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4035242d-f18b-4709-bb6e-951753bf8b42%2F95de33cc-1e83-48d9-9b9a-bd6d4eae7efd%2Fu5m0i_processed.png&w=3840&q=75)
Transcribed Image Text:1) Consider the following linear system:
x+2y + 4z = 2
-2x −3 y −6 z= −1
-
x +2y+dz =d
For what values of d does this system have: (i) no solutions; (ii) exactly one
solution; (iii) infinitely many solutions?
[Hints: If you are going to divide by an expression, make certain that it is not
equal to zero. Also, if you come across a term that is the difference of two
squares, consider factoring it. In each case, list all values of d.]
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