Problem 4 (Rotation w.r.t. Current Frame): A frame {B3 is located initially coincident with frame (A)...
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
1. The orientation of a reference frame F2 is obtained from the reference frame F by a 2 - 3 - 1 rotation sequence, with angles Oy, 0, and ex: • A rotation dy about the y-axis of frame F1, • A rotation 0, about the z-axis of the intermediate frame Fi, • A rotation 0x about the z-axis of the transformed frame Ft. (note that we used rotation sequence 3 – 2 – 1 in class to find the...
Problem 3 1. Prove that B (51, b2, b3,-4} {а, ег#3+ега, +6) is the basis for R4. al 2. Find 1 4 0 0 0 : 0 0 0 00 0 b 3. Consider the map T: R4-W with B-matrix B a 。), Find the standard matrix 1896 of T Problem 3 1. Prove that B (51, b2, b3,-4} {а, ег#3+ега, +6) is the basis for R4. al 2. Find 1 4 0 0 0 : 0 0 0 00...
CE 160 Problem 1(15% 4 k B 12 ft AR 24 ft The statically determinate rigidly connected frame has a pin support at point A and a roller support at point C. The frame is subjected to a point load at point B. The frame is rigidly con- nected at point B. If the bending stiffness of column AB is 40,000 k-ft and the bending stiffness for beam BC is 60,000 k-ft, find: I. (596) The bending moment diagram for...
I Undertand how the first two rows came about in the matirx, but I dont underatnd how the last row was calculated. How did it go from -4b1 +b3 to -2b1-b2+b3 Problem 5. (20) Find conditions(s) on bi, bz and by in order to guarantee that the linear system 13 consistent *+y-2=b 2x - 4y + 5z = b2 4x - 2y + 3z = b3 Solution. We use the augmented matrix and reduce the system. 11 1 -16] [1...
1. a A frame B is rotated 60° about the y-axis, 45° about the n-axis, then translated 4 and 6 units relative to the x- and z-axes respectively, then rotated another 30° about the a-axis. Find the new location (10 marks) and orientation of the frame. 0 0 -1 3 -1 0 0 4 1. a A frame B is rotated 60° about the y-axis, 45° about the n-axis, then translated 4 and 6 units relative to the x- and...
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
Let T : R2 → R2 be the linear transformation given by T(v) = Av that consists of a counterclockwise rotation about the origin through an angle of 30 2, Find the matrix that produces a counterclockwise rotation about the origin through an angle of 30°. Be sure to give the EXACT value of each entry in A. a. b. Plot the parallelogram whose vertices are given by the points A(0, 0), B(4, 0), C(5, 3), and D 1, 3)...
Problem 4. Determine if the following sets B1, B2, B3, B4 and Bs are open, closed, compact or connected. (You don't need to prove your findings here) a) B1 =RQ. b) We define the set B2 iteratively: C1 = [0, 1] C2 =[0,1/4] U [3/4, 1] C3 =[0,1/16] U [3/16, 4/16] U [12/16, 13/16] U [15/16, 1] Then B2 = n Cn. NEN c) B3 = U (2-7,3+"). nn +1 NEN d) f:R+R continuous and V CR closed. B4 =...
PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z = 3. (a) Find its moments and products of inertia relative to the origin. (b) The particle undergoes pure rotation about the z axis through a small angle a. Show that its moments of inertia only vary as a if a1. (C2 PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z...