Theory question 111
Matrices and DeterminantsGiven that M: (x, y) → (7y, 3x − y) and N: (x, y) → (2x − y, 5x + 3y), (a) write down matrices M and N of the linear transformations; (b) find the image of P(2, −3) under the linear transformation N followed by M; (c) find the coordinates of the point Q whose image is Q′(2, 4) under the linear transformation N.
Show the model answer
Model answer
Matrices written row by row:
(a) M = (0 7 / 3 −1), N = (2 −1 / 5 3).
(b) N(2, −3) = (7, 1); then M(7, 1) = (7, 20). (MN = (35 21 / 1 −6).)
(c) 2x − y = 2 and 5x + 3y = 4 give x = 10/11, y = −2/11. Q(10/11, −2/11).
Explanation
'N followed by M' means apply N first.