B Apply

Evaluate each determinant.

38. [ 4 5 − 4 4 ] . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 5 , row2 column 1 , negative 4 , column 2 4 , end matrix
39. [ − 3 10 6 20 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 10 , row2 column 1 , 6 , column 2 20 , end matrix
40. [ − 1 2 2 − 2 8 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative , 1 half , column 2 2 , row2 column 1 , negative 2 , column 2 8 , end matrix
41. [ 6 9 3 6 ] . matrix with 2 rows and 2 columns , row1 column 1 , 6 , column 2 9 , row2 column 1 , 3 , column 2 6 , end matrix
42. [ 0 2 − 3 1 2 4 − 2 0 1 ] . matrix with 3 rows and 3 columns , row1 column 1 , 0 , column 2 2 , column 3 negative 3 , row2 column 1 , 1 , column 2 2 , column 3 4 , row3 column 1 , negative 2 , column 2 0 , column 3 1 , end matrix
43. [ 5 1 0 0 2 − 1 − 2 − 3 1 ] . matrix with 3 rows and 3 columns , row1 column 1 , 5 , column 2 1 , column 3 0 , row2 column 1 , 0 , column 2 2 , column 3 negative 1 , row3 column 1 , negative 2 , column 2 negative 3 , column 3 1 , end matrix
44. [ 4 6 − 1 2 3 2 1 − 1 1 ] . matrix with 3 rows and 3 columns , row1 column 1 , 4 , column 2 6 , column 3 negative 1 , row2 column 1 , 2 , column 2 3 , column 3 2 , row3 column 1 , 1 , column 2 negative 1 , column 3 1 , end matrix
45. [ − 3 2 − 1 2 5 2 1 − 2 0 ] . matrix with 3 rows and 3 columns , row1 column 1 , negative 3 , column 2 2 , column 3 negative 1 , row2 column 1 , 2 , column 2 5 , column 3 2 , row3 column 1 , 1 , column 2 negative 2 , column 3 0 , end matrix

46. Think About a Plan Use matrices to find the area of the figure below.

    

    • What shapes do you know how to find the area of?
    • Can the polygon be broken into these shapes?
    • How many shapes will you need to break the polygon into?
47. Writing Suppose A = [ a b c d ] eh equals . matrix with 2 rows and 2 columns , row1 column 1 , eh , column 2 b , row2 column 1 , c , column 2 d , end matrix  has an inverse. In your own words, describe how to switch or change the elements of A to write A − 1 . eh super negative 1 end super , .
48. If matrix A has an inverse, what must be true?
    1. A A − 1 = I eh , eh super negative 1 end super , equals i
    2. A − 1 A = I eh super negative 1 end super eh equals i
    3. A − 1 I = A − 1 eh super negative 1 end super i equals , eh super negative 1 end super
    1. I only
    2. II only
    3. I and II only
    4. I, II, and III

49. Geometry Use matrices to find the area of the figure below. Check your result by using standard area formulas.

    

Determine whether each matrix has an inverse. If an inverse matrix exists, find it. If it does not exist, explain why not.

50. [ 1 4 1 3 ] . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 4 , row2 column 1 , 1 , column 2 3 , end matrix
51. [ 4 7 3 5 ] . matrix with 2 rows and 2 columns , row1 column 1 , 4 , column 2 7 , row2 column 1 , 3 , column 2 5 , end matrix
52. [ − 3 11 2 − 7 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 3 , column 2 11 , row2 column 1 , 2 , column 2 negative 7 , end matrix
53. [ 2 0 0 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 0 , row2 column 1 , 0 , column 2 2 , end matrix
54. [ − 2 1 − 1 2 0 4 0 2 5 ] . matrix with 3 rows and 3 columns , row1 column 1 , negative 2 , column 2 1 , column 3 negative 1 , row2 column 1 , 2 , column 2 0 , column 3 4 , row3 column 1 , 0 , column 2 2 , column 3 5 , end matrix
55. [ 2 0 − 1 − 1 − 1 1 3 2 0 ] . matrix with 3 rows and 3 columns , row1 column 1 , 2 , column 2 0 , column 3 negative 1 , row2 column 1 , negative 1 , column 2 negative 1 , column 3 1 , row3 column 1 , 3 , column 2 2 , column 3 0 , end matrix
56. [ 0 0 2 1 4 − 2 3 − 2 1 ] . matrix with 3 rows and 3 columns , row1 column 1 , 0 , column 2 0 , column 3 2 , row2 column 1 , 1 , column 2 4 , column 3 negative 2 , row3 column 1 , 3 , column 2 negative 2 , column 3 1 , end matrix
57. [ 1 2 6 1 − 1 0 1 0 2 ] . matrix with 3 rows and 3 columns , row1 column 1 , 1 , column 2 2 , column 3 6 , row2 column 1 , 1 , column 2 negative 1 , column 3 0 , row3 column 1 , 1 , column 2 0 , column 3 2 , end matrix

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