Date: Mar 2, 2013 3:44 AM
Author: Bill Rowe
Subject: Re: An unknown Greek matrix
On 2/28/13 at 9:26 PM, marshfeldman@gmail.com wrote:

>Forgive me if this is obvious, but I'm a Mathematica newbie and have

>given up trying to figure this out any other way.

>I have the following defined matrices:

>A = {{5, 0}, {0, 10}} B = {{6, 3}, {1, 12}}

>and a row vector:

>L = {{1, 1}}.

>I don't know how to use Greek here, so I'll use "Lambda" as the name

>of a row vector whose name is really the Greek letter lambda

>capitalized and "lambda" for as the name of the elements of Lambda

>subscripted, with the elements really being lower-case versions of

>the Greek letter lambda and subscripts indicated by appending _n,

>where n is the subscript (e.g. lambda_1 is lowercase lambda

>subscripted with 1). In other words,

You can enter Greek letters in one of two ways. Either by using

the full name, i.e.,

\[Lambda]

or by using the esc key as follows

esc l esc

Subscripts can also be entered using simple key strokes. But I

am not going to do that here. Mathematica can be made to use

subscripted variables as you would see in a text book. But IMO,

usage of subscripted variables is more of an advanced

Mathematica technique and more trouble than it is worth.

>Lambda = {{lambda_1, lambda_2}}.

>Now given the following equation, solve for Lambda:

>Lambda B = Lambda A + L.

>Also, display the elements of Lambda as

>lambda_1 = -1 lambda_2 = 2.

>Can one do this in Mathematica? How?

So, I will show a solution without the subscripted variables.

Also, it is highly recommended not to use a single upper case

letter as a variable name. There are a several built-in

functions which are named with a single upper case letter.

Avoiding the use of single upper case letters as variable names

ensures you will not have conflicts with built-in symbols and

save you a lot of grief in the long run.

So, here are your matrices

In[1]:= a = {{5, 0}, {0, 10}};

b = {{6, 3}, {1, 12}};

In[3]:= l = {{1, 1}};

In[4]:= lambda = {{x, y}};

Now to set up the equation

In[5]:= eq = lambda.b == lambda.a + l

Out[5]= {{6*x + y, 3*x + 12*y}} == {{5*x + 1, 10*y + 1}}

note the use of a double = which defines an equation in

Mathemtica and the usage of '.' to tell Mathematica I want to

perform a matrix multiplication rather than and element by

element multiplication

and the solution can be found with

In[6]:= Solve[eq, {x, y}]

Out[6]= {{x -> -1, y -> 2}}