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匿名使用者
匿名使用者 發問時間: 科學數學 · 5 年前

一個旋轉矩陣問題

Find the single matrix A that represents the sequence of consecutive transformations:

anticlockwise rotation through π/6 about the z-axis, followed by reflection in the plane x=z, followed byinversion, and followed by shortening along the positive direction of x-axis to one third of its initial value

1 個解答

評分
  • 麻辣
    Lv 7
    5 年前
    最佳解答

    1.Rotation angle = π/6B = [cos(π/6) sin(π/6) 0; -sin(π/6) cos(π/6) 0; 0 0 1]*A = [√3/2 1/2 0; -1/2 √3/2 0; 0 0 1]*A= Tq * A

    2.Reflection by z = xC = [0 0 1; 0 1 0; 1 0 0]*B= Tr * B= Tr * Tq * A

    3.Inversion = 'D = (Tr * Tq)' * A= Tq' * Tr' * A

    4.Shorten E = [2/3 0 0; 0 1 0; 0 0 1]*D = Ts * D= Ts * Tq' * Tr' * A

    5.Tq'=?= [√3/2 -1/2 0; 1/2 √3/2 0; 0 0 1]

    6.Tr'=?= Tr= [0 0 1; 0 1 0; 1 0 0]

    7.T = Ts * Tq'* Tr' = ?= [√3/3 -1/3 0; 1/2 √3/2 0; 0 0 1] * Tr'= [0 -1/3 √3/3; 0 √3/2 1/2; 1 0 0]

    8.E = (Ex Ey Ez) = ?= [0 -1/3 √3/3; 0 √3/2 1/2; 1 0 0]*(Ax Ay Az)= (-Ay/3 + √3*Az/3; √3*Ay/2 + Az/2; Ax)

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