You are to start with two arbitrary but independent
3x3matrices in sl(3,r), such that no zero entries lie on the
maindiagonal. with these two matrices a0 and a1, you will then
generatesuccessive lie brackets until you have constructed a basis
forsl(3,r).
what is the dimension of sl(3,r)? remember that you mustdiscard
any brackets during the process of construction, which
aredetermined to be linearly dependent upon any brackets that
werepreviously generated.
finally, produce any arbitrary(non-basis element)b fromsl(3,r)
and write it as a linear combination of your generatedbasis
element.