Let LA be the linear map from R2 to R2 defined by LA (i) = Av, and let LB be the linear map from ...
(1 point) Let S be a linear transformation from R2 to R2 with associated matrix A= Let T be a linear transformation from IR2 to R2 3 1 ]' Determine the matrix C of the composition ToS
Let T be a linear map from R3[z] to R2[z] defined as (T p)(z) =
p'(z). Find the matrix of T in the basis:
4 points] Let T be a linear map from Rals] to R12] defined as (TP)(z) = p,(z). Find the matrix of T in the basis: in R2[-]; ~ _ s, r2(z) (z-s)2 in R2 [2], where t and 8 are real numbers. T1(2 Find coordinates of Tp in the basis lo, 1, 12 (if p is...
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
Let T : R3 → R2 be a linear map. Recall that the image of T, Im(T), is the set {T(i) : R*) (a) Suppose that T(v)- Av. Describe the image of T in terms of A Using this description, explain why Im(T) is a subspace of R2. (b) What are the possible dimensions of Im(T)? (c) Pick one of the possible dimensions and construct a specific map T so that Im(T) has that dimension.
SF78. Consider the linear map T : Rn → Rm defined by T(v) = Av where A=12 43 6 12-7 (a) What is m? (b) What is n? (c) The image of T is a subspace of R. What is i? (d) The image of T is isomorphic to R. What is j? e The kermel of T is isomorphic to Rt. What is k7 (f) The kernel of T is a subspace of R. What is ?
4. (22 points) Let To : R2 R2 be the linear transformation that rotates each point in IR2 about the origin through an angle of θ (with counterclockwise corresponding to a positive angle), and let T,p : R2 → R2 be defined similarly for the angle φ. (a) (8 points) Find the standard matrices for the linear transformations To and To. That is, let A be the matrix associated with Tip, and let B be the matrix associated with To....
2. Let T be the linear transformation from P2 to R2 defined by 20 – 201 T(@o+at+aat) = | 0o + a1 + a2 Find a basis for the range of T.
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...
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)...
Linear Algebra
1. Consider the following map T : R2 → R. Is T a linear transformation? Explain 2. Suppose that A is a 3 × 4 matrix. The following elementary row operation has the same effect as multiplying a matrix E on the left of A. What is that matrix E?