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(1 point) Let A- [7 ] Define the linear transformation T: R2 + R by T)...
(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
(1 point a. The linear transformation T : R2 → R2 is given by: Ti (x, y) = (2x + 9y, 4x + 19y). Find T1x, y). 「-i(x, y) =( x+ y, x+ b. The linear transformation T2 : R' → R' is given by: T2(x, y, z) (x + 2z,2r +y, 2y +z) Find (x, y, z). T2-1(x,y,z)=( x+ y+ z, x+ y+ z, x+ y+ z)
Question Let T : R2 + Rº be a linear transformation with PT(x) = x2 – 1. Determine/Compute the linear transformation T2 : R2 + R?, UH T(T(v)).
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
Let ai, a2 , аз, bị, b2P3 R. Define T : R3 R2 by Prove T is a linear transformation.
(1 point) Let in = [] and v2 = [:3] Let T : R2 + R2 be the linear transformation satisfying TW) = ( 13 ) and Tlőz) = 1 3 х Find the image of an arbitrary vector -(:) -
(1 point) Let T : P3-> P3 be the linear transformation such that Find T(1). T(x). T(r2), and T(az2 + bz+ c), where a, b, and c are arbitrary real numbers. T(1) = T(z) = T(r2) Note: You can earn partial credit on this problem.
Let T: R2 + R2 be a linear transformation with PT(x) = 22 – 1. Determine/Compute the linear transformation T2 : R2 + R2, vH T(T(v)). Show all your work for full credit.