Which row operations are normal operators? If a row operation is not a normal operator, given an example of such an operator and find a vector u such that ||Au||2 does not equal ||A*u||2.

Mickey Mantle played for the New York Yankees for 18 years from 1951 to 1968. Year by year he hit the following numbers of home runs: 13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18. We represent these as a vector x in R by making the following assignmemt: x <-c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Define the vector y by the assignment y <- cumsum(x) Define the variable w using the assignment W <-714-y Define z with the assignment z <-c(X,Y,W) x, y, w and z are vectors. Answer the following using R code. a) Calculate the minimum value of z. b) Calculate the sum of the squares of the elements in z. c) Calculate the sample mean of z. [ d) Calculate the sample variance of z. e) Calculate the sample standard deviation of z f) What is the 18th element of w? (value of w[18]) g) Calculate the sample variance of x. h) Calculate the sample variance of 5*x| i) What is the length(# of elements) in 5*x j) How many unique(different) values…

(a) Find all the real numbers x such the vectors (178) 1+x and 1 (*+¹) 1 are orthogonal.

= If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V2 = W₁ + W3 and V3 = W₁ + W2 independent or dependent? Show all of your work.