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#1, 2, 3, 4 Problem 1 The linear transformation T : x + Cx for a vector x ERP is the composition of a rotation and a scaling if C is given as c=[. 0 0.5 -0.5 0 - [1] (1) Find the angle o of the rotation, where --<<, and the scale factor r. (2) If x without computing Cx, sketch x and the image of x under the transfor- mation T (rotation and scaling) in the RP plane....
The linear transformation T :x + Cx for a vector x € R is the composition of a rotation and a scaling if C is given as 0 0.5 -0.5 0 C-[ 1. You can consider the recurrence Xx+1 = Cxx,k=0,1,2,..., as the repeated application of the transformation T. What is X2020 if Xo = o = [1]:
Solve the initial value problem with 4 x'(t) = A, fort > O with x(0) = Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction and/or repulsion. x(o)= [1] A-[18 -16] -2 - 4 10 -16 2 -120 1 a. x(t)= (0,0) is a saddle point 5 2 120 b. x(t)= 1 + 6 le -61 (0,0) is an attractor 5 C. x(t)= o[1]...
Solve the initial value problem with x'(t) = A, for t20 with x(0)= Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction and/or repulsion. -2 -4 A= 10 -16 127 a. X(t)= is a saddle point b. X(t)= 121 + 6 (0,0) is an attractor 1 --[1]26. (0,0) --[] $]e=121+6[71]e-, (0,0) is an attractor d. x(e) = - [] -e[1]26. (0,0) is repeller e....
5.7.3 Solve the initial value problem x'(t) Ax(t ) for t2 0, with x(0) = (3,2). Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x' Ax. Find the directions of greatest attraction and/or repulsion 12 16 A= 8 12 Solve the initial value problem. x(t) 5.7.3 Solve the initial value problem x'(t) Ax(t ) for t2 0, with x(0) = (3,2). Classify the nature of the origin as an...
4AHW8: Problem 18 Previous Problem Problem List Next Problem (1 point) To every linear transformation T from R2 to R2, there is an associated 2 x 2 matrix. Match the following linear transformations with their associated matrix. 1. Counter-clockwise rotation by 1/2 radians 2. Reflection about the y-axis 3. Reflection about the line y=X 4. Clockwise rotation by 1/2 radians 5. Reflection about the x-axis 6. The projection onto the x-axis given by T(x,y)=(x,0) 1 0 A. B. 1 0...
Let T: P2 --> R2 be the linear transformation such that T(x+1)=(1,1), T(x2)=(1,0) and T(x-1)=(0, 1). Find T(2+x+x2).
Let T: P2 + P, be a linear transformation for which T(1) = 3 - 2x, 7(x) = 9x – x2, and 7(x2) = 2 + 2x2. Find T(2 + x - 8x?) and T(a + bx + cx?). T(2 + x - 8x2) T(a + bx + cx) II
(1 point) Let T : P3-> P3 be the linear transformation such that Find T(1). T(x). T(r2), and T(az2 + bz+ c), where a, b, and c are arbitrary real numbers. T(1) = T(z) = T(r2) Note: You can earn partial credit on this problem.
Let T: R2 + R2 be a linear transformation with PT(x) = 22 – 1. Determine/Compute the linear transformation T2 : R2 + R2, vH T(T(v)). Show all your work for full credit.