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謝真 asked in 科學數學 · 6 years ago

高二數學 矩陣

Update:

圈起來的選項為該題的答案

1 Answer

Rating
  • 6 years ago
    Favorite Answer

    第一張圖:

    將右方矩陣代表的意義代入

    x=2

    y=1

    z=-3

    x+3y-6z=c

    2+3+18=c

    c=23

    ax+4y+z=5

    2a+4-3=5

    2a=4

    a=2

    3x+y+bz=19

    6+1-3b=19

    -3b=12

    b=-4

    a+b+c=2+(-4)+23=21

    第二張圖

    1.

    利用三階行列式

    有無限多組解 代表△=△x=△y=△z=0

    代入△x=0

    |k+2 -1 2|

    |5 -5 0 |

    |k -3 -2 |

    =10k+20-30+0+10k-10+0=0

    20k-20=0

    k=1

    2.

    另矩陣A

    [a d g]

    =[b e h]

    [c f i ]

    det(A)

    |a d g|

    =|b e h|

    |c f i |

    det(3A)

    |3a 3d 3g|

    =|3b 3e 3h|

    |3c 3f 3i |

    將第一二三行的3提出

    |a d g|

    =27|b e h|

    |c f i |

    =27det(A)

    3.

    將最右方矩陣代表的意義代入

    x+z=6

    y=3

    2y-2z=-4

    得到z=5,x=1

    x+y+z=1+3+5=9

    代入第二個矩陣

    x-y+z=c

    c=1-3+5=3

    ax-y+2z=9

    a-3+10=9

    a=2

    x+by-z=-1

    1+3b-5=-1

    3b=3

    b=1

    a+b=2+1=3

    第三張圖

    a11為今日點滷肉飯的客人,明天依然點滷肉飯的機率

    a12為今日點肉羹麵的客人,明天改點滷肉飯的機率

    a21為今日點滷肉飯的客人,明天改點肉羹麵的機率

    a22為今日點肉羹麵的客人,明天依然點肉羹麵的機率

    轉移矩陣A為

    [0.7 0.4]

    [0.3 0.6]

    [0.7 0.4][1] [0.7]

    [0.3 0.6][0]=[0.3]

    明天這位客人依然點滷肉飯的機率為0.7,改點肉羹麵的機率為0.3

    [0.7 0.4][0.7] [0.61]

    [0.3 0.6][0.3]=[0.39]

    後天這位客人依然點滷肉飯的機率為0.61,改點肉羹麵的機率為0.39

    長時間看來

    [0.7 0.4][ k ] [ k ]

    [0.3 0.6][1-k]=[1-k]

    0.7k+0.4-0.4k=k

    0.4=0.7k

    k=4/7=0.5714...

    1-k=3/7=0.4285..

    長期來看,此客人點滷肉飯的機率為0.5714>0.5

    此人點肉羹麵的機率為0.4285<0.5

    (1)有2種可能

    1.先點滷肉飯再點肉羹麵,機率為0.7*0.3=0.21

    2.先點肉羹麵再點滷肉飯,機率為0.3*0.4=0.12

    機率為0.21+0.12=0.33

    (2)

    0.3*0.6*0.6=0.108

    (3)

    如上,為0.61

    (4)

    如上,為0.4285

    (5)

    如上,為0.5714

    正確答案應為(1)(4)(5)

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