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From the two images provided, here's a summary of the mathematical problem described:

### Problem Description:
There are two families, **A** and **B**, and the information about their composition and daily nutritional needs is as follows:

- **Family A**: 
  - 1 man
  - 1 woman
  - 2 children
- **Family B**: 
  - 2 men
  - 2 women
  - 4 children

### Nutritional Allowances:
1. **Calories (per day)**:
   - Men: 2400 gm
   - Women: 1900 gm
   - Children: 1800 gm

2. **Protein (per day)**:
   - Men: 55 gm
   - Women: 45 gm
   - Children: 33 gm

### Task:
- Represent the above information using matrices.
- Use matrix multiplication to calculate the **total requirement of calories and protein for each family**.

---

I'll now represent this information in matrix form and calculate the totals. Let's set up the two matrices:

1. **Matrix for Family Members** (Each row represents Family A and Family B, and columns represent the number of men, women, and children):

\[
\text{Family Matrix} = \begin{pmatrix} 
1 & 1 & 2 \\ 
2 & 2 & 4 
\end{pmatrix}
\]

2. **Matrix for Nutritional Allowances** (Each row represents the allowances for calories and protein, and columns represent men, women, and children):

\[
\text{Nutritional Matrix} = \begin{pmatrix} 
2400 & 1900 & 1800 \\ 
55 & 45 & 33 
\end{pmatrix}
\]

Now, let's compute the total calorie and protein requirement for both families using matrix multiplication.

\[
\text{Total Nutritional Requirement} = \text{Family Matrix} \times \text{Nutritional Matrix}
\]

Let me calculate that for you.It seems there's a misalignment in the matrix dimensions. The nutritional matrix should have two rows (for calories and protein) and three columns (for men, women, and children). To correctly compute the total nutritional requirements, the rows and columns need to be transposed. I'll fix the setup and recalculate.The total nutritional requirements for each family are as follows:

1. **Family A**:
   - **Calories**: 7,900 gm/day
   - **Protein**: 166 gm/day

2. **Family B**:
   - **Calories**: 15,800 gm/day
   - **Protein**: 332 gm/day

Would you like a more detailed explanation of how the calculations were done? Feel free to ask any further questions!

Here are some related questions for practice:

1. How would the requirements change if the number of men, women, or children in a family were different?
2. How would you set up a matrix if there were more nutritional requirements, like fats and carbohydrates?
3. Can you compute the total protein needed for a third hypothetical family with 3 men, 3 women, and 5 children?
4. What are the benefits of using matrices in solving such real-life problems?
5. How would the calculation change if the requirements were given in different units?

**Tip**: When dealing with multiple categories and variables, matrices simplify calculations by structuring data clearly and enabling efficient computation with operations like multiplication.

There are two families A and B. Family A has 1 man, 1 woman, and 2 children, while Family B has 2 men, 2 women, and 4 children. The recommended daily allowances for calories are: Men: 2400 gm, Women: 1900 gm, Children: 1800 gm. For protein: Men: 55 gm, Women: 45 gm, Children: 33 gm. Represent the information using matrices and calculate the total requirements of calories and protein for each family using matrix multiplication.

Learn how to use matrices to represent and calculate the total daily nutritional requirements of two families using matrix multiplication. This problem involves key mathematical concepts, including matrix multiplication, and provides a practical application of these skills.

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