Orthogonal Complements. We Will use the same matrices that appear in Problem 3 from Part I. Let W = Span({31, ..., 37}), the columns ofA. In other words, W = colspace(A). a. Find a basis for Wi. As part of your solution, explain which rref you should use, R or R'. Hint: Wand Wi are from the same ambient space. b. State the Dimension Theorem for Orthogonal Complements in general. c. State dlm(W) and dim(Wi). (1. Verify the Dimension Theorem for Wand Wi. Fidget Spinner. Find the matrix for rote, Where 6 = cos'1(21/29). Keep the entries as exact fractions. Use the matrix to nd rote (( 5, 8 )). Again, keep the entries as exact fractions. Use your calculator to approximate cos1(2l/29) in degrees. Then plot (5, 8 ) and rot9((5, 8 )), and verify that the angle between them is approximately 9 (you don't need to use a protractor). \fNow, you are also given that the rref of AT is: 04 20 3 1 . 0000 5 100305 0101 001 000000 000000 000000 R