Question
Two families A and B have men, women and children. Using matrix multiplication, find total calorie and protein requirements.
Solution
Step 1: Family Matrix
\[ F = \begin{bmatrix} 4 & 6 & 2 \\ 2 & 2 & 4 \end{bmatrix} \]Step 2: Nutrition Matrix
\[ N = \begin{bmatrix} 2400 & 45 \\ 1900 & 55 \\ 1800 & 33 \end{bmatrix} \]Step 3: Multiply
\[ R = F \times N \] \[ = \begin{bmatrix} 4 & 6 & 2 \\ 2 & 2 & 4 \end{bmatrix} \begin{bmatrix} 2400 & 45 \\ 1900 & 55 \\ 1800 & 33 \end{bmatrix} \]Step 4: Calculate
Family A: \[ 4×2400 + 6×1900 + 2×1800 = 24600 \text{ calories} \] \[ 4×45 + 6×55 + 2×33 = 576 \text{ grams protein} \] Family B: \[ 2×2400 + 2×1900 + 4×1800 = 15800 \text{ calories} \] \[ 2×45 + 2×55 + 4×33 = 332 \text{ grams protein} \]Final Answer
Family A: 24600 calories, 576 g protein
Family B: 15800 calories, 332 g protein
Awareness
✔ Balanced diet is essential for proper health
✔ Different age groups need different nutrition
✔ Proper planning avoids malnutrition
✔ Matrix helps in real-life planning like diet, budgeting
✔ Awareness of nutrition improves quality of life