I have done it clearly for you. Kindly go through.
Find the transition matrix Ps4R where S = {(1,-1,0), (-1, 2, -1),(0,1,1)} and R= {(0,1,–1), (1,0,1),(1,0,0)}....
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)
7. The matrix 1 0 0 PE 0 3 2 011 is the transition matrix from what basis B to the basis {(1,1,1), (1, 1,0), (1,0,0)} of R3?
(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
EXERCISE 1 [2.5/10] a) [1/10] Let B- [(0,1,-1), (1,1,1), (1,0,1)) be a basis of IR3. Calculate the coordinates of the vector -el+e2 with respect to the basis B. (B. {e!, e2, e) is the canonical basis) [1.5/10] Let B-lul., иг, из} and B'-fu', ua",_} be two bases of R3. where : b) 3 Calculate the change of basis matrix from B to B' EXERCISE 1 [2.5/10] a) [1/10] Let B- [(0,1,-1), (1,1,1), (1,0,1)) be a basis of IR3. Calculate the...
Please show all work. 11. Find the transition matrix from B to B'. {(1,0), (0,1)}, B {(1,1), (5,6)} B =
Transformation T:R' -»R',T(x,y, z) = (x+y,x-z)nd v=< 1,-1,2 > 8. ar iven B <1,1,1>,< 1,0,1 ><-1,0,1>},B^ = {<1,1>,<1,0 >},and B, = {<1,0>,< 1,1>} B to Biand from B to B2 a) Find the Transition matrix from b) Find v],T[v];,7[v] c) Find v,and [v]p d) What did you conclude? Transformation T:R' -»R',T(x,y, z) = (x+y,x-z)nd v= 8. ar iven B ,},B^ = {,},and B, = {,} B to Biand from B to B2 a) Find the Transition matrix from b) Find...
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and ((1,-1). (2,0). 11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and...
1 0 0 The matrix P= 0 7 4 is the transition matrix from what basis 8 = 0 2 2 to the basis {(1,1,1),(1,1,0),(1,0,0)) for R?? (0,0,0 Edit (0.0.0 Edit (1.0.0 Edit
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
5. (4) Construct (if possible) a matrix satisfying both conditions below. If not, explain why (a) The null space consists of all linear combinations of (2,2,-1,0) and (-2, 1,0,1) (b) The column space contains (1, 1,0, 1) and (0, 1, 1,-1) and whose null space contains (1,0,1,1) and (0,1,-1,0)7 5. (4) Construct (if possible) a matrix satisfying both conditions below. If not, explain why (a) The null space consists of all linear combinations of (2,2,-1,0) and (-2, 1,0,1) (b) The...