(* Solving Ax = b *) 
(* To run on command line:  math -run "<<matrix.math" *)
(* The above line assumes that math kernel is aliased to "math" *)
(* For example, on my machine alias math='/Applications/Mathematica.app/Contents/MacOS/MathKernel' *) 
(* or simply use << matrix.math once math kernel is already running *) 

Print["----Solving Tx = b  --- "]


(* define matrix size. matrix T is n x n *) 
n=3

(* uncomment the line below if you want to have the same sequence of random numbers each time you run the code *) 
 (* SeedRandom[1] *)   

(* define a nxn matrix T with random entries from -1 to 1 *) 
(* T = RandomReal[{-1,1},{n,n}] *) 

(*random vector *) 
b = RandomReal[{-1,1},{n,1}]

(* example of a  3x3 matrix as a table of numbers *) 

(* T = {{10000000, 0.1, 0.1},{0.1, 1, 0.1},{0.1, 0.1, 0.0000001}}  *) 

(* a tri-diagonal matrix with random entries *) 
T = SparseArray[{Band[{1, 2}] -> RandomReal[{-1,1}], Band[{1, 1}] ->
RandomReal[{-1,1}], Band[{2, 1}] -> RandomReal[{-1,1}]}, n]

Print["----here is the matrix --- "]
Print[MatrixForm[T]]

Print["----here is the vector --- "]
Print[MatrixForm[b]]

Print["----Condition number --- "]
Print[LinearAlgebra`MatrixConditionNumber[T]]


(* solve Tx = b *) 
S=LinearSolve[T,b] 

Print["----here is the solution of Ax = b --- "]
Print[S]

(* compute the residual *)  
Res = Norm[T.S -b] 
Print["----the residual --- "]
Print[Res]

Print["--------- memory used in GB ----------" ] 
Print[MaxMemoryUsed[]*0.000000001]
Exit[]