Matrix multiplication applied to a football scoring problem from 1966, calculating final scores based on touchdowns, field goals, safeties, and extra points.

We are given a word problem involving matrix multiplication to calculate the final scores of two NFL teams — Washington and New York — based on their scoring plays.

Given:

- Scoring values:
- Touchdown (TD) = 6 points
- Field Goal (FG) = 3 points
- Safety (S) = 2 points
- Extra Point (EP) = 1 point

- Scoring summary:

| | TD | FG | S | EP |
|-----------|----|----|---|----|
| Washington| 10 | 1 | 0 | 9 |
| New York | 6 | 0 | 0 | 5 |

We are to use matrix multiplication to compute the total score for each team.

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Step 1: Represent the data as matrices

Let’s define:

- A 2×4 matrix $ A $ representing the number of each type of scoring play by each team:

$$
A = \begin{bmatrix}
10 & 1 & 0 & 9 \\
6 & 0 & 0 & 5
\end{bmatrix}
$$

- A 4×1 column vector $ B $ representing the point values of each scoring type:

$$
B = \begin{bmatrix}
6 \\ 3 \\ 2 \\ 1
\end{bmatrix}
$$

Now, we multiply $ A \times B $ to get the total score for each team.

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Step 2: Perform matrix multiplication

$$
A \times B =
\begin{bmatrix}
10 & 1 & 0 & 9 \\
6 & 0 & 0 & 5
\end{bmatrix}
\times
\begin{bmatrix}
6 \\ 3 \\ 2 \\ 1
\end{bmatrix}
$$

We compute each entry of the resulting 2×1 matrix:

#### For Washington (first row):
$$
(10)(6) + (1)(3) + (0)(2) + (9)(1) = 60 + 3 + 0 + 9 = 72
$$

#### For New York (second row):
$$
(6)(6) + (0)(3) + (0)(2) + (5)(1) = 36 + 0 + 0 + 5 = 41
$$

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Final Answer:

$$
\text{Final Score} = \begin{bmatrix}
72 \\
41
\end{bmatrix}
$$

So, the final score was:
- Washington: 72 points
- New York: 41 points

✔ This matches historical records of the highest-scoring NFL game in 1966.

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✔ Summary:

Using matrix multiplication:
- We multiplied the scoring counts matrix by the point value vector.
- Result: Washington scored 72, New York scored 41.