Theory question 112
Matrices and DeterminantsQuestion 12 is for candidates in Sierra Leone and Gambia
(a) Given that A = (3 4; 2 5) and X = (3 4), evaluate XA
(b) A linear transformation T maps A = (3 4) → A1(−6, 8) and B(5, 2) → B(−10, 4). Find the: (i) Matrix of T, (ii) Image of the point k(1, −1) under T.
Show the model answer
Model answer
(a) XA = (3×3 + 4×2 3×4 + 4×5) = (17 32)
(b)(i) Let T = (a b; c d)
3a + 4b = −6 and 5a + 2b = −10 give a = −2, b = 0
3c + 4d = 8 and 5c + 2d = 4 give c = 0, d = 2
T = (−2 0; 0 2)
(ii) T(1; −1) = (−2; −2), so the image is (−2, −2)
Explanation
Write T with unknown entries and form simultaneous equations from the two given images.