Solve for the steady State
[0.905, 0, 0.03,
0.075, 0.88, 0,
0, 0.11, 1.0]
My Working:
[0.905, 0, 0.03, [x [x
0.075, 0.88, 0, y = y
0, 0.11, 1.0] z] z]
therefore
0.11y + z = z
0.11y = 0
y = 0
0.075x + 0.88y = y
0.075x + 0.88(0) = 0
x = 0
therefore z must also be 0?
I
think you mean the following:
. . . . .\(\displaystyle \mbox{Solve for the steady-state matrix:}\)
. . . . .\(\displaystyle \left[\begin{array}{rrr}0.905&0&0.03\\0.075&0.88&0\\0&0.11&1.0\end{array}\right]\)
. . . . .\(\displaystyle \mbox{My working:}\)
. . . . .\(\displaystyle \left[\begin{array}{rrr}0.905&0&0.03\\0.075&0.88&0\\0&0.11&1.0\end{array}\right]\left[\begin{array}{c}x\\y\\z\end{array}\right]\, =\, \left[\begin{array}{c}x\\y\\z\end{array}\right]\)
. . . . .\(\displaystyle \mbox{Therefore:}\)
. . . . .\(\displaystyle 0.11y\, +\, z\, =\, z\)
. . . . .\(\displaystyle 0.11y\, =\, 0\)
. . . . .\(\displaystyle y\, =\, 0\)
. . . . .\(\displaystyle 0.075x\, +\, 0.88y\, =\, y\)
. . . . .\(\displaystyle 0.075x\, +\, 0.88(0)\, =\, 0\)
. . . . .\(\displaystyle x\, =\, 0\)
. . . . .\(\displaystyle \mbox{Therefore }\, z\, \mbox{ must also be }\, 0?\)
Is the above correct? Thank you!
