Linear Algebra Stuff for MathILy

The easiest way to define a matrix in Mathematica is to make nested arrays of numbers.

A = {{0,1,2,9},{5,10,-15,1},{3,6,-8,0}}

Remember, a matrix can represent a system of linear equations.Instead of doing all the algebra of solving these by hand (you know, adding together equations, or subtracting them, or multiplying them by constants, all that stuff) you can ask the computer to do it for you:

RowReduce[A]

But that's not very pretty...

MatrixForm[RowReduce[A]]

A Small Pile of Potentially Useful Commands with No Explanatory Text

v1 = {1,3,2};
1/2 v1

v2= {4,1,5};
v1+v2

Norm[{3,1,2}]

{4,3,67,2}.{8,0,2,1}

Transpose[A]
MatrixForm[Transpose[A]]

MatrixRank[A]

B = {{1,0,0,0},{1,1,1,1},{1,-1,1,-1},{1,3,9,27}};

IB =Inverse[B];
MatrixForm[IB]

IB.{3,0,2,6}