Theory question 111
Matrices and Determinants(a) Given that P = (2 4 / −9 1) and Q = (1 −1 / 3 −2), find PQ + 2Q
(b) A bag contains 8 red balls and some white balls, all of the same size. If the probability of drawing at random a white ball from the bag is half the probability of drawing a red ball, find the number of white balls in the bag.
Show the model answer
Model answer
(a) PQ = (2+12 −2−8 / −9+3 9−2) = (14 −10 / −6 7)
2Q = (2 −2 / 6 −4)
PQ + 2Q = (16 −12 / 0 3)
(b) Let w = white balls: w/(8 + w) = ½ × 8/(8 + w) ⇒ w = 4 white balls
Explanation
Multiply rows of P by columns of Q.