1. Consider the rotation in Fig 1. What is the rotation matrix? Fig 1 2 3 3 1. Consider the rotation in Fig 1. What is the rotation matrix? Fig 1 2 3 3
(4) (a) Determine the standard matrix A for the rotation r of R
3 around the z-axis through the angle π/3 counterclockwise. Hint:
Use the matrix for the rotation around the origin in R 2 for the
xy-plane. (b) Consider the rotation s of R 3 around the line
spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a
basis of R 3 for which the matrix [s]B,B is equal to A from (a).
(c) Give...
3. In-Class Exercises (75 minutes (a) Find the rotation matrix that rotates the vector A into the vector B, where, in the home repre- sentation, 134 ー4 (b) Find the inverse of the rotation matrix c) What happens to the scalar product of A and B under this rotation?
3. In-Class Exercises (75 minutes (a) Find the rotation matrix that rotates the vector A into the vector B, where, in the home repre- sentation, 134 ー4 (b) Find the inverse...
2. Consider a reflection in the y-axis, dilation factor of In(2), rotation through, and a contraction factor of V7. A. Determine the matrix that defines this transformation. B. Determine the image of under this transformation.
2. Consider a reflection in the y-axis, dilation factor of In(2), rotation through, and a contraction factor of V7. A. Determine the matrix that defines this transformation. B. Determine the image of under this transformation.
7. Fig.2. Shows a 3-bus network. Obtain the Impedance Matrix (ZBus) by following the order of buses (i.e. 0-1-2-3) 0.20 0.50 0.50 0.20 0.20 Reference bus Fig. 2 Three bus network.
R (a) Write the rotation matrix that describes the frame (A) with respect to the frame (B. (3 points) 10 (b) If the point 5find P (2 points)
R (a) Write the rotation matrix that describes the frame (A) with respect to the frame (B. (3 points) 10 (b) If the point 5find P (2 points)
Consider the two rotations shown. Calculate the rotation matrix for each trans- formation (ể x,y,z to ēm.y,z, then ê' r,y,z to ēr,y,z), then calculate the required rotation matrix to move from ēr,y,z to ēr,y,z. Find the eigenvalues and eigenvectors of this final matrix. Ae
Consider the matrix 3 -2 1 A 1 2 -1 1-2 3 a) Find the characteristic polynomial of A and show that A has an eigenvalue at zero. Find the other two eigenvalues of A b) Find eigenvectors of A corresponding to all eigenvalues c) Can you diagonalize this matrix?
Consider a three-node quadratic element in one dimension with unequally spaced nodes (Fig. 2). (a) Obtain the B matrix. (b) Consider an element with x1=0, x2=1/5 and x3=1 Evaluate strain & in terms of u2 and u (u0), and check what happens when s approaches 0. (c) If you evaluate K by one-point quadrature using B EADB for same coordinates as in (b) and constrain node 1 (i.e. 0), is K invertible?
Problem 1: Consider the matrix 3 -2 -11 A = -1 2 -1 |-1 -2 3 a) Find the characteristic polynomial of A and show that A has an eigenvalue at zero. Find the other two eigenvalues of A. b) Find an eigenvector of A corresponding to all eigenvalue. c) Can you diagonalize this matrix?