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12.5 Solutions to Determinants Problems

    1. -10     -6 - 4 = -10

    2.  36      30 - (-6) = 36

    3. -211    (18 + 0 - 168) - (40 + 0 + 21) = -211

    4.  153    (0 + 75 + 14) - (0 - 84 + 20) = 153

    5. -2        (0 + 0 + 0) - (27 + 0 - 25) = -2

    6.  solution steps is one method.
    7.  solution steps
    8.   solution steps

    1. x1 = 1    x2 = -1    x3 = 2

      A, B_1, B_2, B_3


    2. x1 = 2    x2 = 1    x3 = -1

      A, B_1, B_2, B_3


  3.   A^-1"

    1. True

      proof


    2. True

      proof


    3. False

      proof

      This is only one example. The students' answers will vary.


    4. True

      proof

      These are equal because cb = bc in scalar multiplication.


  5. Use a generic matrix and expansion by minors.

    proof


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