List five of the elements of the sets:
(a) a={t < −1,5> | t∈r > , and
(b)b= {p < 2, −3, 0> + q< −1, 1, 0> | p, q ∈ r> .

a) <-1,5>, <1,-5>, <2,-10>, <-2,10>, <-100,500> are elements in set A

b) <1,4,0>, <0,0,0>, <2,3,0>, <18,32,0>, <8,7,0> are elements in set B

Step-by-step explanation:

a) Set A defines an infinite line in  , that means, 2-D space, that has a direction defined by the vector <-1,5>, and a parameter t that allows to get all the points in space in that direction both sides of the origin because t can be any real number.

We can get all the points of that line by plugging numbers into the parameter, that multiplies each component of the original vector, for example, plugging 1, -1, 2, -2 and 100, gives us the following points in space:  

1: <-1,5>

-1: <1,-5>

2: <2,-10>

-2: <-2,10>

100: <-100,500>

b) Set B defines an infinite plane in , that means, 3-D space, and it is defined by the vectors <2,-3,0> and <-1,1,0>, and parameters p and q, both being any independent from each other real number.

We can get all points in space belonging to that plane by plugging numbers into the parameters, for example, a: 1 and 1, b: 0 and 0, c: 1 and 0, d: 10 and 2, e: 3 and -2:

a: 1*<2,3,0>+1*<-1,1,0> = <1,4,0>

b: 0*<2,3,0>+0*<-1,1,0> = <0,0,0>

c: 1*<2,3,0>+0*<-1,1,0> = <2,3,0>

d: 10*<2,3,0>+2*<-1,1,0> = <18,32,0>

e: 3*<2,3,0>+(-2)*<-1,1,0> = <8,7,0>

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

you can't solve x because it is 2 linear equation and you only have one equation