?How should the coefficients a, b, and c be chosen so that the system\(a x+b y-3

Chapter 1, Problem 12

(choose chapter or problem)

How should the coefficients a, b, and c be chosen so that the system

$a x+b y-3 z=-3$

$-2 x-b y+c z=-1$

$a x+3 y-c z=-3$

has the solution $x=1, y=-1$, and $z=2$?

Equation Transcription:

$ax\ +\ by\ -\ 3z\ =\ -3\$

$-2x\ -\ by\ +\ c\ z\ =\ -1\$

$ax\ +\ 3y\ -c\ z\ =\ -3$

$x\ =\ 1,\ y\ =\ -1$

$z\ =\ 2$

Text Transcription:

ax + by - 3z = -3

-2x - by + c z = -1

ax + 3y -c z = -3

x = 1, y = -1

z = 2

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