Which of the following vectors are perpendicular to the lines r=<0,1,1> + t<1,1,0> and r=<1,0,0>+t<0,1,1>? a)...
(b) Apply the perceptron algorithm to the following pattern classes 5 Wi (0,0,0)T, (1,0,0)7, (1,0,1)T, (1,1,0)T\ W2 ((0,0,1)T, (0,1,1)T, (0,1,0)T, (1,1,1)T Let C 1 and W(1) = (-1, -2, -2, 0)1. Sketch the decision surface
Which of these planes are perpendicular to lines r=(0,1,1) + t(1,1,0)? a) x+y+z=2 b) x+y+z=3 c) y+z=2 d) x+y=2
6. Let S : R + R3 be the linear transformation which satisfies |(1,0,0) = (1,0,–3), S(0,1,0) = (0,-1,0) and S(0,0,1) = (1,-1, -2). Give an expression for S(x, y, z). 4 Marks] Let S be the basis (1,0,0), (0,1,0), (0,0,1) for R3 and let T be the basis (0,0,1), (0,1,1), (1,1,1) for R. Compute the change of basis matrix s[1]7. (b) Compute the matrices s[S]s and s[ST. 18 Marks)
1. Given force F-xi 4zj Path 1: (0,0,0) to (0,1,1) Path 2: (0,1,1) to (1,1,0) Path 3: (1,1,0) to (0,0,0) 5yk acts following the path: . Sketch the motion in Cartesian coordinate Write the parametric equation for each path Calculate the total work done by force F which is moving from Path 1 to 3 2. A vector M is defined by M-x2yi xyj and region R corresponds to Sketch the region of R in Cartesian coordinate . Evaluate the...
marks] The position of a particle is given as a function of time by r(t)=(1-cos(27t)i+ (1-t)sin(2nt)j+ 4tk with i (1,0,0), j = (0,1,0) andk = (0,0,1) the Cartesian basis vectors of R3. (a) Sketch the particle trajectory from t 0 tot= 1, as a 3D perspective plot and as the 2D projection onto the xy-plane. (b) Determiner(t) as a function of time t. (c) Is r'(t) greater for t 0 than it is for t 1? Justify your answer. marks]...
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass function P(x, y, z) given below. Be sure to full justify your answers and show ALL work. P(0,0,0) = 2,3 P(0,0,1) 33 P(0,1,0) = P(1,0,0) = 32 P(1,0,1) = P(1,1,0) = 32 a. Find the marginal probability mass function for 2, pz(2). b. What is E[X | Y = 0]? P(0,1,1) = 4 P(1,1, 1) = 32
Which of the following sets of vectors does not span R?? Select one: a. (1,3, 2), (1,0,1),(0, 2, 2) b. (2,3,4), (6,0,7), (0,9,5) C. ((6,7, 1), (2, 2, 3), (1,1, 2) d. (1,4,6), (2,3,1), (1,1,0)
Problem 2 (3 marks) There are 2 point charges Qt) at (1,0,0) and Q2(t) at (-0.5, 0, 0). Given current I flows from Q2t) to Qı(t) Find the line integral of H along the square close path C crossing (0,-1,1), (0,1,1), (0,1,-1), (0,-1,-1). Problem 2 (3 marks) There are 2 point charges Qt) at (1,0,0) and Q2(t) at (-0.5, 0, 0). Given current I flows from Q2t) to Qı(t) Find the line integral of H along the square close path...
Let T: R3 - R be a linear transformation such that T(1,1,1)= (2,0,-1) T(0,-1,2)=(-3,2,-1) T(1,0,1)= (1,1,0) Find T (2,-1,1). a) (10,0,2) b) (3,-2-1) c)(2,2,2) d) (-3,-2, -3)
I only have a few hours to answer and send. I would appreciate if you help. Thank you so much. a 1. Let V = {[ :a+c=b+ =b+ d} une and T:V + R with T ([: 1) = a +c. Cd a) Find a basis for the kernel of T. dim(Ker(T)) =? (10P) b) Find a basis for the image of T. dim(Im(T)) =? (10P) c) Is T an isomorphism? (5P) 2. Let T = {(2,3), (3, 2)} be...