Berechne die Determinanten der folgenden Matrizen:

´G = ((6,5),(1,8))´

´H = ((2,3,5), (-1,4,2), (3,-2,2))´

´J = ((2,-3,1,4), (1,3,-2,2), (3,2,3,-3), (4,1,2,2))´

Approach

´det(G) = det( ((6,5),(1,8)) ) = 6 *8 - 5 * 1 = 43´

´det(H) = det(((2,3,5),(-1,4,2),(3,-2,2))) = ´´2 det( ((4,2),(-2,2)) ) - 3 det( ((-1,2),(3,2)) + 5 det( ((-1,4),(3,-2)) )´ ´= 2 * (8+4) - 3 * (-2-6) + 4 * (2-12) = ´´2 * 12 - 3 * -8 + 5 * -10 = ´´24 + 24 - 50 = -2´

´det(J) = det(((2,-3,1,4), (1,3,-2,2), (3,2,3,-3), (4,1,2,2)))´

´= 2 det( ((3,-2,2),(2,3,-3),(1,2,2)) ) - det( ((-3,1,4),(2,3,-3),(1,2,2)) ) + ´´3 det( ((-3,1,4),(3,-2,2),(1,2,2)) ) - 4 det( ((-3,1,4),(3,-2,2),(2,3,-3)) )´

´= 2 * 52 - (-39) + 3 * 52 - 4 * 65 = 39´


Solution

  • ´det(G) = 43´ ´det(H) = -2´ ´det(J) = 39´

  • URL:
  • Language:
  • Subjects: math computer graphics
  • Type: Calculate
  • Duration: 15min
  • Credits: 3
  • Difficulty: 0.4
  • Tags: matrix determinant
  • Note:
    HPI, 2014-05-19, Computergrafik 1, Aufgabe 8d
  • Created By: adius
  • Created At:
    2014-07-28 19:58:42 UTC
  • Last Modified:
    2014-07-28 19:58:42 UTC