Consider the ordered bases B = ace V of upper triangular 2 x 2 matrices. Find the transition matrix from C to B. -C33²2) and=6³1²3 =]B = Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = 1 Find M. and C = ( ) for the vector

d) All of the above LQ9. Suppose A is the 4 by 4 identity matrix with its lASt column removed.The projection matrix P that projects the vector b = (1, 2,3, 4) onto the column space of A is %3D a) the 4 by 4 identity matrix. b) the 3 by 3 identity matrix. c) the 4 by 4 matrix whose fourth column and row are zeros with a 3 by 3 identity matrix sitting in its upper left Comer.

Let y = 0 and u = Into A enter UTU. Into B enter UUT. Into Center projwy. Into D enter (UUT)y. T let U be the 2x1 matrix whose only column is u, and let W span(u).

If you keep the same basis vectors but put them in a different order, the change of basis matrix B is a __ matrix. If you keep the basis vectors in order but change their lengths, B is a __ matrix.

Let B and C be bases for R2. If B = {(-1, –1), (3, 4)} and the change-of-basis matrix from B to C is Pg-c find C.

Let A= {a;.a2,a3} and B = {b,.b2.b3} be bases for a vector space V, and suppose a, = 5b, - – 2b3. a. Find the change-of-coordinates matrix from A to B. b. Find (xlg for x= 5a, + 6a2 + az. a P B-A b. xlg =0 (Simplify your answer.)

3= b, ,b2} and C= (c,.c2} be bases for a vector space V, and suppose b, = - 6c, + 5c2 and b2 = - 4c, +2c2. a. Find the change-of-coordinates matrix from B to C. b. Find (x]c for x = - 5b, + 3b2. Use part (a). a. P = C-B b. (xlc (Simplify your answers.)