1.) Determine whether the set, together with the indicated operations is a vector space. If it is not, then identify all of the ten vector space axions which fail. The set {(x, y): x > 0, y > 0} with the standard operations in R2

Evaluate the following vector expression: a = [3 -6 -2] -3 Calculate 3(ax + az) and enter your answer in the answer box below

This is a Linear Algebra problem. Please explain each step clearly, no cursive writing.

Loblolly is a built-in R dataset that that records the growth of Loblolly pine trees. We are interested in the height column of Loblolly. The values in the height column can be converted into a vector of name x by the assignment: x <- Loblolly$height We can see the values in x by typing x and Return or Enter. Remember x <- Loblolly$height After this assignment, we can see the first six values in x by typing head(x) and Return or Enter a. Give the R code to assign the values in in the height column of Loblolly to the vector named x. (Easy-see above) b. Calculate the interquartile range of x using the R, IQR() function. c. Calculate the sum of the squares of the values in x. d. Calculate the sample mean of x. e. Calculate the sample variance of x. f. Calculate the sample standard deviation of x. f. Using R, calculate a trimmed mean of x. [ h.Enter your R script in the box below.