Problem 3. Construct a single 2 x 2 matrix which defines the transformation on R?, and...
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle of counterclockwise as viewed fronm the positive z-axis and then shifts the result by-5 in the x-direction, 4 in the y-direction, and -2 in the z-direction, is given by The image of (-4,-5,-1) under this transformation is 0 , and Z = 1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle...
Find the matrix for the linear transformation which reflects every 2-dimensional vector across the y axis and hen rotate by an angle of T/4
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...
Assume that is a linear transformation. Find the standard matrix of T. T: R2R2 first rotates points through - radians and then reflects points through the horizontal Xy-axis. (Type an integer or simplified fraction for each matrix element. Type exact answers, using radicals as needed.)
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax that reflects a vector (1), 12) about the Tz-axis. (b) Find a linear transformation SR2 R2 such that T(x) = Bx that rotates a vector (2, 2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the matrix of this transformation explicitly. How...
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:R? → Rº be the linear transformation that first rotates points clockwise through 30° (7/6 radians) and then reflects points through the line y = 2. Find the standard matrix A for T. A=
(1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across the x- axis, shifts the result by 1 in the x-direction, -1 in the y-direction, and -1 in the z-direction, and then expands the y coordinate by a factor of 5 is given by A= The image of (5,-4,-1) under this transformation is , and Z = (1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across the x- axis, shifts the...
(4) (a) Determine the standard matrix A for the rotation r of R 3 around the z-axis through the angle π/3 counterclockwise. Hint: Use the matrix for the rotation around the origin in R 2 for the xy-plane. (b) Consider the rotation s of R 3 around the line spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a basis of R 3 for which the matrix [s]B,B is equal to A from (a). (c) Give...
A 2 x 2 matrix A is associated with the transformation that reflects vectors in the plane across the line y = 2x. Sketch the vector field (use your discretion and draw vectors until you believe that you have captured the big picture) corresponding to A. In other words, for every ~w, we place A ~w at the head of ~w.