# Proper format for writing basis in linear algebra

1. Jan 27, 2009

### Dell

if i am asked to find a basis for a vector subspace, am i meant to jus write one possible option, for example

basis: (8,0,0)(0,6,0)(0,0,2)

or am i supposed to write the whole span

basis: sp{(8,0,0)(0,6,0)(0,0,2)}

or am i meant to write it with parameters

basis: a(8,0,0) + b(0,6,0) + c(0,0,2)

or am i meant to write it in its simplist form

basis: (1,0,0)(0,1,0)(0,0,1)

and how about when i am asked to present all possible basises

2. Jan 27, 2009

### CompuChip

The basis is a set which consists of three vectors, so I would write:
B = { (8,0,0), (0,6,0), (0,0,2) }
just like you would write set of three numbers like S = {1, 6, 12}.
If you want to give a normalized basis (or that is asked of you), you can write
$\hat B$ = { (1, 0, 0), (0, 1, 0), (0, 0, 1) }

The vector space V which is spanned by that basis is denoted by
V = sp(an) B = sp( { (8,0,0), (0,6,0), (0,0,2) } )
which means that you can write an arbitrary vector v in V as a linear combination
a(8,0,0) + b(0,6,0) + c(0,0,2)

Is that clear?