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.

all it means is function 3

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for