Find all x in Rª that are mapped into the zero vector by the transformation x-Ax for the given matrix A. 1 3 11 4 102-4 01 3 4 -2 2 2 8 A= Select the correct choice below and fill in the answer box within your choice. OA. There is only one vector, which is x = OB. X3 OC. x₁ OD. x₁

Consider the following matrices: and A = B 12 3 4 2 = 1 Find the products AB and BA or say why they are not defined.

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.

17. Find the 4 by 3 matrix A that represents a right shift: (x1,x2, x3) is transformed to (0, x1,x2, x3). Find also the left shift matrix B from R4 back to R³, transforming (x1,x2, x3, x4) to (x2, x3, x4). What are the products AB and BA?