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Re: An unknown Greek matrix
Posted:
Mar 2, 2013 3:44 AM
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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}}
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