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
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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?
[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.]
Transcribed Image Text: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? [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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