Hi i have this problem it's on a past paper.  The main problem is with
the second part of the question the bit worth 12 marks but any help is
appreciated.



Let V be Real^4 and let W be Real^3, and let T be the linear map which
sends (x,y,z,t) in V to
(2x+y+z, 3x, 4x-y-z) in W.

Write down the matrix A of T. Find new bases for V and W
for which which T has matrix of coordinates R3x4 whose entries
rij satisfy r11 = r22 = 1, and rij = 0 otherwise. Is there a
linear relation between the rows of A?

rij is r subscript ij, likewise with r11 and r22

Cheers