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.

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.