\fPlease check for yourself that Q is, indeed, an ONB. Also define the 3-vectors v = (4, 2v2, 3v/2) and w = (x, (y - z) / V2, (y + z)/ V2). (Here, x, y, and z are stand-ins for scalars. ) (a) Find the coordinate representations [vlo and [wo. (b) Let P be the elementary projector for the line {tq2 : t E R} along the plane {x ( R' : q!x =0}. Write the results of Pq1, Pq2, and Pq3. (c) With P as defined in part (b), explain how you can use the results from the previous parts to deduce the result of [Pw]Q. Verify your answer by writing the result of [Pv]o (using what you know about [v]Q). (d) Let Me be the elementary dilator given by Mc = I + (c -1)P, where P is as defined in part (b), and c is a non-zero scalar. Explain how you can use the results from the previous parts to deduce the result of [Mcw]Q. Verify your answer by writing the result of [Mcve (using what you know about [vje)