Consider the following. T is the reflection through the origin in R2: T(x, y) = (-x,...
Consider the following. Tis the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= 1 (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of v and its image. у 6 у 6 V 5: 5 41 4 3 3 T(v) 2 2 11 1 X 1 -6 -5 -4 -3 -2 -1 -A 2...
Tis the reflection through the origin in RP: 7x, y) = (-X, Y), (3,2). (a) Find the standard matrix A for the linear transformation T. A- It (b) Use A to find the image of the vector v T(V) (c) Sketch the graph of vand its image. 3 T(v) 2 2 1 -3 2 - - 2 -1 2 1 3 -1 -1 -2 T(v) -31 -3 O T (v) 3 2 2 11 1
Consider a linear transformation F : R2→R2
In lectures it is shown that the reflection in a subspace can be calcu- lated by Rw(u) = 2 prw(u) – u. Use this formula to find the standard matrix of the linear transformation described above. and hence deter- mine the image of the reflection of the y-axis in the line y = 2x.
Consider the following. T is the projection onto the vector w = (3, 1) in R2: : T(v) = projwv, v = (1, 4). (a) Find the standard matrix A for the linear transformation T. A = (b) Use A to find the image of the vector v. T(v)
Consider the following T is the reflection in the y-axis in R2: T(x, y) (-x, y), v (2, -5) (a) Find the standard matrix A for the linear transformation T (b) Use A to find the image of the vector v (e) Sketch the graph of v and its image T (v) 5-4-3-21 T (v) T(v) 6 -5-4-3-2 6-5-4-3-2-1 239-lab 3 (2)pages F1 Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for...
linear algebra
Let T: R2 R2 be a reflection in the line y = -x. Find the image of each vector. (a) (-3,9) (b) (5, -1) (c) (a,0) (d) (o, b) (e) ( ed) (f) (9)
1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
Find the standard matrix for the linear transformation T. T(x, y) = (3x + 2y, 3x – 2y) Submit Answer [-70.71 Points] DETAILS LARLINALG8 6.3.007. Use the standard matrix for the linear transformation T to find the image of the vector v. T(x, y, z) = (8x + y,7y - z), v = (0, 1, -1) T(v)
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)...
Let T: R3 → R2 T(x, y, z) = (x + y,y+z) a. Is T a linear transformation? b. Find the matrix A of T C. Find the dimension of NUT and image T