The linear transformation () = [ 1 0 0 1 ] is a reflection of 2 about a line. What features of the matrix tell you this? Find the equation of the line. 2. Find the matrix of the orthogonal projection onto the line l given by = 3. Begin by determining a unit vector on the line l. Use the matrix you just obtained to determine each of the following: a. Proj (1 ) = b. Proj ([ 2 2 ]) = c. Proj ([ 3 1 ]) = The vectors you obtained above should all lie on the line = 3. In other words, their -components should be three times their -components. Check that this is true. Your answer in part (c) ought to have been 0 because there is a special relationship between the line = 3 and the vector [ 3 1 ]. What is this relationship and why should this relationship cause the projection of [ 3 1 ] onto the line = 3 to equal 0? 3. Find the transformation matrix for a reflection about the -plane in 3 . No algebra is required here!! Draw the -, -, and -axes and the unit vectors 1, 2, and 3. Use your picture to determine (1), (2), and (3). (You should be able to figure out the components of these vectors.) Recall that the columns of the transformation matrix are (1), (2), and (3). Let B represent the matrix that you found above. Use your matrix to determine the reflection of the vector [ 1 2 3 ] across the -plane. Does your answer make sense?