(a) Suppose we have a data set consisting of three points in 2 R 2 : ( 1 , 3 ) , ( 2 , 6 ) , ( 3 , 9 ) (1,3),(2,6),(3,9). How many principal components does this data set have? Write down the first principal component. (b) Given the SVD of matrix = = [ 1 2 3 4 3 1 7 9 10 ] A=UV T = 1 4 7 2 3 9 3 1 10 = [ 0.222 0.364 0.905 0.270 0.914 0.301 0.937 0.178 0.301 ] , = [ 16.180 0 0 0 2.862 0 0 0 0 ] , = [ 0.486 0.599 0.637 0.716 0.145 0.682 0.501 0.788 0.358 ] U= 0.222 0.270 0.937 0.364 0.914 0.178 0.905 0.301 0.301 ,= 16.180 0 0 0 2.862 0 0 0 0 ,V T = 0.486 0.716 0.501 0.599 0.145 0.788 0.637 0.682 0.358 Write down the matrix that is the best rank-1 approximation to A. You don't need to calculate