Solving 3 Equations for w in Matrix Form

[andybham]

Is it possible to put these three equations into a matrix equation

w*a = b -2a + e
w*b = c -2b + a
w*c = d -2c + b

of the style w*u = T*u where u is a vector, u = {a, b, c} and T is a matrix. w is just a number.

 

[mathman]

What are d and e? If they are really different and not typos, then you will need T*u+v=w*u, where v is the vector (e,0,d) and ------------------------------------------------
------------------------------------------------------------------
T=
-2 1 0
1 -2 1
0 1 -2
--------------------------------------------------------------------------------

 

[andybham]

no they are not typos, could I not use

T = -2 1 e/c
1 -2 1
d/a 1 -2

or is that just stupid?

 

[radou]

Is it possible to put these three equations into a matrix equation

w*a = b -2a + e
w*b = c -2b + a
w*c = d -2c + b

of the style w*u = T*u where u is a vector, u = {a, b, c} and T is a matrix. w is just a number.

What exactly are the unknowns in your equations? a, b, c? If so, then

(2 + w)a - b = e
-a + (2 + w)b - c = 0
-b + (2 + w)c = d ,

which can be written as
$$\left(\begin{array}{ccc}2+w & -1 & 0\\-1 & 2+w & -1\\0 & -1 & 2+w\end{array}\right) \left(\begin{array}{ccc}a \\b\\c\end{array}\right)=\left(\begin{array}{ccc}e \\0\\d\end{array}\right)$$.