Linear Algebra
Your NAME HERE

1.  Blah blah some very easy Linear Algebra Question....

5+5

Alt+7 is your friend to make a text bracket.....

2. Junk, stuff, more stuff... another easy question....

A = {{2,1,3},{-4,2,0}}

A//MatrixForm

RowReduce[A]

%//MatrixForm

RowReduce[Transpose[A]]

%//MatrixForm

T = Transpose[{{1,0,1,0},{0,1,0,1},{1,1,0,0},{1,-1,0,0}}]

RowReduce[{{1,0,1,0},{0,1,0,1},{1,1,0,0},{1,-1,0,0}}]//MatrixForm

2{1,0,1,0}+3{0,1,0,1}-{1,1,0,0}+5{1,-1,0,0}

S = Transpose[{{1,4,3,0},{2,5,1,6},{2,4,0,2},{5,5,2,5}}]

RowReduce[{{1,4,3,0},{2,5,1,6},{2,4,0,2},{5,5,2,5}}]

T//MatrixForm

S//MatrixForm

Inverse[S].T//MatrixForm

T.{{0},{1},{3},{4}}

Inverse[S].{{7},{0},{0},{1}}

-(70/83)*{1,4,3,0}-(142/83){2,5,1,6}+(55/166){2,4,0,2}+(176/83){5,5,2,5}