# Matrix equation

1. Mar 7, 2007

### 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.

2. Mar 7, 2007

### 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 ------------------------------------------------
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T=
-2 1 0
1 -2 1
0 1 -2
--------------------------------------------------------------------------------

Last edited: Mar 7, 2007
3. Mar 7, 2007

### 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?

4. Mar 7, 2007

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