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...
please provide clear drawings for each 5. Let T9,b) (x, y) = (x +a, y +b) and Rę be the reflection about a line l. a. T<1.2> Rc=y (3,5) = b. Rc=yo T<1,2> (3,5) = c. If P is the point (2,1), find the image of P: under the reflection R-axis: under R2=3: under the half turn Riso about the origin: under the half turn R180 about the center (1,1).
Consider the following. T is 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= (b) Use A to find the image of the vector v. T(V) =
in a reflection the image of the line y-2x=3 is the line 2y-x=9.find the axis of reflection.
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...
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
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...
Please help, and provide some explanation if possible! Thank you :) (1) Answer the following questions (a) Let T : R3 → R2 be such that (i) Find a matrix A such that T(E) Az. (i) Find T(2,-3,5). (iii) Is the transformation T invertible? YES No (b) The smiley face shown at the top of the figure is transformed by various linear transformations represented by matrices A - F. Find out which matrix does which transformation. Write the letter of...
6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z. what is A, the standard matrix of T1? (b) Suppose T : R2R is the counterclockwise rotation by 8 J. What is A2, the standard matrix of T2? (c) What is the image of (2,-4) under T- Ti o T2? 6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z....