William and Michael's stock holdings are given by the matrix At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix .

Question

William and Michael's stock holdings are given by the matrix  At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix  .

Quizplus · Accepted Answer

To obtain the total value of William's stocks, we need to multiply the first matrix by the first row of the second matrix and sum the products. Similarly, to obtain the total value of Michael's stocks, we need to multiply the first matrix by the second row of the second matrix and sum the products.

William's total value = (11)(42) + (4)(41) + (-2)(34) + (8)(37) = 1164
Michael's total value = (9)(42) + (10)(41) + (7)(34) + (3)(37) = 1231

Therefore, the total value of their stocks combined is 1164 + 1231 = 2395.

To obtain the matrix of the total value of their stocks, we need to multiply the second matrix by a scalar (in this case, the scalar is 2395).

B is the only choice that reflects this calculation, as it is obtained by multiplying each element of the second matrix by 2395.

William and Michael's Stock Holdings Are Given by the Matrix