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4) At the high school championship game, the Cougars beat the Lions 31 to 17. The total score came from 14 scoring plays. The scoring plays consisted of touchdowns, extra-point kicks, and field goals. Touchdowns are worth 6 points each, extra-point kicks are worth 1 point each, and field goals are worth 3 points each. The number of touchdowns was equal to the number of extra-point kicks. Write a linear system to represent this game. Use matrices to then solve the system. How many touchdowns, extra-point kicks, and field goals occurred in the game? 5) Evaluate each determinant. a. b. C.
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Answer #1

Solution : ( 5 )

( a )

46 1

Matrix determinant according to formula: det ad-bc Cl

2*6-4*1

12 - 4

8

Hence, detĢ)-8

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Solution : ( 5 )

( b )

504

=0*det egin{pmatrix}3&0 3&4end{pmatrix}-4* det egin{pmatrix}1&0 -1&4end{pmatrix}+5* det egin{pmatrix}1&3 -1&3end{pmatrix}

4

0*(12-0) _ 4 * (4-0)+5*(3+3)

=0*(12)-4* (4)+5* (6)

=0-16+30

=14

mathrm{Hence,quad}det egin{pmatrix}0&4&5 1&3&0 -1&3&4end{pmatrix}=14

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Solution : ( 5 )

( c )

det egin{pmatrix}-2&3&4 1&6&9 8&9&-3end{pmatrix}

=-2* det egin{pmatrix}6&9 9&-3end{pmatrix}-3* det egin{pmatrix}1&9 8&-3end{pmatrix}+4* det egin{pmatrix}1&6 8&9end{pmatrix}

=-2* (6left(-3 ight)-9*9)-3* (1*left(-3 ight)-9*8)+4*(1*9-6*8)

一一2 * (-18-81)-3*(-3-72) + 4 * (9-48)

=-2left(-99 ight)-3left(-75 ight)+4left(-39 ight)

=198+225-156

267

mathrm{Hence,quad}det egin{pmatrix}-2&3&4 1&6&9 8&9&-3end{pmatrix}=267

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