A trader keeps rice, wheat and pulses (in bags) in two godowns G1 and G2. The opening stock, the bags received and the bags sold during a week are given by the matrices O, R and S (rows: rice, wheat, pulses; columns: G1, G2):
\(O = \begin{bmatrix} 40 & 25 \\ 30 & 35 \\ 20 & 15 \end{bmatrix},\quad R = \begin{bmatrix} 10 & 15 \\ 20 & 5 \\ 5 & 10 \end{bmatrix},\quad S = \begin{bmatrix} 35 & 20 \\ 28 & 30 \\ 18 & 12 \end{bmatrix}\)
The matrix of the stock left at the end of the week is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\begin{bmatrix} 15 & 20 \\ 22 & 10 \\ 7 & 13 \end{bmatrix}\)
Stock left = opening stock + bags received − bags sold. All three matrices have the same order \(3 \times 2\), so this is done element by element:
\(O + R - S\)
\( \displaystyle = \begin{bmatrix} 40 + 10 - 35 & 25 + 15 - 20 \\ 30 + 20 - 28 & 35 + 5 - 30 \\ 20 + 5 - 18 & 15 + 10 - 12 \end{bmatrix} \)
\( \displaystyle = \begin{bmatrix} 15 & 20 \\ 22 & 10 \\ 7 & 13 \end{bmatrix} \)
For example, 22 bags of wheat are left in G1.