a) (1 point) What is rank(A) 3 b) (a point) Find matrix B such that A-8 or 8-A results in the same matrix as A, but with ts first 2 columns swapping 2 3 places (A-B or BA 5 4 6) c) (1 point) What is the dot (inner) product between u and v d) (1 point) What is the outer product between u and v What is the difference between mean and median? hinn is 3. Name 3 ways in which we can perform an exploratory data analysis of a numerical attribute? 4. You are given a matrix A of size 100 x 5 whose rank(A) - S. You are given a matrix B of size 5 x 20 made up of random numbers. a) (0.5 points) What is the size of A-B? b) (1.5 points) What is the largest possible value of rank(A-8)? Why? 5. You are given the following data set saved as pandas object f. Try to guess whatis the output of a) dffear.value counts) Origin Year Size USA 2016 1.5 2011 3 b) pit,scatter r Year',dEt'size' Japan 2017 4.0 USA 2017 | 2.5 USA 2016 3.0 c) np.corrcoef (dfIl'Year, 'Size'11.7) pdcrosste ,dEl Year']) e) d?pivot table (values- 5421, index-"origin"]) 201b 2017