The opening stock of two shops P and Q for a week is given by the matrix A, and the number of items sold during the week by the matrix B, where
\(A = \begin{bmatrix}40&25&12\\35&30&18\end{bmatrix}\) and \(B = \begin{bmatrix}28&14&9\\22&19&11\end{bmatrix}\).
In each matrix the first row is for shop P, the second row is for shop Q, and the columns are for shirts, trousers and jackets in that order. The total number of items left unsold at shop Q at the end of the week is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 31
The items left unsold are given by the difference A − B, taken element by element:
\( \displaystyle A - B = \begin{bmatrix}40 - 28&25 - 14&12 - 9\\35 - 22&30 - 19&18 - 11\end{bmatrix} = \begin{bmatrix}12&11&3\\13&11&7\end{bmatrix} \)
The second row is for shop Q, so the total number of items left at shop Q is
\(13 + 11 + 7 = 31\)