The table summarizes the scoring of a football game between Team A and Team B. A touchdown (TD) is worth 6 points, a field goal (FG) is worth 3 points, a safety (S) is worth 2 points, and a point after touchdown (PAT) is worth 1 point. Use matrix multiplication to find the final score.
TD FG S PAT
Team A 3 2 1 0
Team B 4 4 1 2
To calculate the final score, we need to multiply the scoring matrix by the point values matrix:
| A1 | | 6 3 2 1 | | 3 2 1 0 | | 6*3 + 3*2 + 2*1 + 1*0 |
| A2 | = | | * | | = | |
| B1 | | 6 3 2 1 | | 4 4 1 2 | | 6*4 + 3*4 + 2*1 + 1*2 |
| B2 | | | | | | |
Calculating the values we get:
A1 = 6*3 + 3*2 + 2*1 + 1*0 = 18 + 6 + 2 + 0 = 26
A2 = 6*4 + 3*4 + 2*1 + 1*2 = 24 + 12 + 2 + 2 = 40
B1 = 6*4 + 3*4 + 2*1 + 1*2 = 24 + 12 + 2 + 2 = 40
B2 = 6*4 + 3*4 + 2*1 + 1*2 = 24 + 12 + 2 + 2 = 40
Therefore, the final score of the game is:
Team A: 26 points
Team B: 40 points.