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Re: An unknown Greek matrix

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  • Subject: [mg129984] Re: An unknown Greek matrix
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 2 Mar 2013 03:44:51 -0500 (EST)
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On 2/28/13 at 9:26 PM, marshfeldman at 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}}




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