Consider the following. T is the clockwise rotation (O is negative) of 60° in R?, v...

Question

Question

Consider the following. T is the clockwise rotation (O is negative) of 60° in R?, v = (1,6). (a) Find the standard matrix A f

math algebra

Answer 1

Answer #1

lau will be given Standard by in matrix A = cos 60° -Sin 60° sin 60° cos 60° 1/2 - 3/2 ta 1312 412 (6) image of vector v = (1

Answer 2

Similar Homework Help Questions

Consider the following. T is the reflection through the origin in R2: T(x, y) = (-x,...

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) =
Consider the following. T is the projection onto the vector w = (3, 1) in R2:...

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)
Finding the Standard Matrix and the Image In Exercises 11–22, (a) find the standard matrix A...

Finding the Standard Matrix and the Image In Exercises 11–22, (a) find the standard matrix A for the linear transformation T, (b) use A to find the image of the vector v, and (c) sketch the graph of v and its image. T is the counterclockwise rotation of 120° in R2, v = (2, 2).

(a) Let T: R2 + R2 be counter clockwise rotation by 7/3, i.e. T(x) is the...

(a) Let T: R2 + R2 be counter clockwise rotation by 7/3, i.e. T(x) is the vector obtained by rotating x counter clockwise by 7/3 around 0. Without computing any matrices, what would you expect det (T) to be? (Does T make areas larger or smaller?) Now check your answer by using the fact that the matrix for counter clockwise rotation by is cos(0) - sin(0)] A A= sin(0) cos(0) (b) Same question as (a), only this time let T...
3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin,...

3. Let T : R2 + Rº be the rotation by 1/2 clockwise about the origin, and let S : R2 + R2 be the shear along the y-axis given by S(x,y) = (x,x+y). (You may assume that these are linear transformations.) (a) Write down, or compute, the standard matrix representations of T and S. (b) Use (a) to find the standard matrix representations of (i) SoT (T followed by S), and (ii) ToS (S followed by T). (c) Let...
Find the standard matrix for the linear transformation T. T(x, y) = (3x + 2y, 3x...

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)

7. Let V be the space generated by the basis B = {sin(t), cos(t), et}. i.e....

7. Let V be the space generated by the basis B = {sin(t), cos(t), et}. i.e. V = span(B). Consider the linear transformation T:V + V defined by T(f(t)) = f"(t) – 2f'(t) – f(t). Find the standard matrix of the transformation. (Hint: Associate sin(t) with the vector (0), and so forth.) 8. Show that B = {t2 – 2, 3t2 +t, t+t+8} is a basis for P2, and find the change of coordinates matrix P which goes from B...
Find an example of a vector space V, and a linear transformation T : V +...

Find an example of a vector space V, and a linear transformation T : V + V such that R(T) = ker(T). Your vector space V must have dimension > 2. You may find it helpful to let V be a euclidean space and T a matrix transformation,
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 countercloc...

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)...

Consider the linear transformation from R² to Rº given by L(21,3) = (31 +232, 21 –...

Consider the linear transformation from R² to Rº given by L(21,3) = (31 +232, 21 – 22). I (a) In the standard basis for R2 and R, what is the matrix A that corresponds to the linear transformation L? (5 points) (b) Let U = {(1,1), (-1,2)}. Find the transition matrix from U to the star dard basis for R. (5 points) (c) Let V = {(1,0), (-1,1)). Find the transition matrix from the standard basis for R2 to V....