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.
QUESTION 2 20 points Save Answer (a) Let A- 101 112 and let T: R 225) T: P = R o via maria menina dentar, TV6 – AR.20 - ( +R be the matrix mapping defined by T(x) = ist wens meer under T is the vector b. and determine whether X is unique (b) Let : R2 + R be the linear transformation that maps the vector - Cinto (6and maps v = ()ino (9) Use the fact that...
2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a geometrical interpretation of T. 2. Let b(1,-1,1). Define T: R3R3 by the mapping: T(x) (x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms (b) Determine the standard matrix representation for T. (c) Give a...
LetM: R2 + R’ be a linear mapping defined by [21 - g] T+2g M L _V_ J What is the standard matrix? 0[2 -1] .11 2 11 ܂ : ܂1 Oro - 7 ܘ 7 0 ܗ ܗ 7 D[ ܗ ܗ 7
Q4. Let L: R2 + Rº be a transformation defined by L (0-2 [3u2 – U1 U1 – U2 -502 (a) Show that I is a linear transformation. (b) Find the standard matrix A of L, and find L ([31]) using the matrix A. (c) Do you think that any transformation T:R2 + R² is linear? (Justify your answer).
2. Let T: P2 + R2 be the linear transformation given by (a-6) T(a + bx + cx?) = | 16+c) Find ker T and im T.
Let b-,-1,1). Define T:RR by the mapping: V3 T(x)-(x b)b (a) Show that T is a linear transformation by verifying the two linear transformation axioms. b) Determine the standard matrix representation for 1 (c) Give a geometrical interpretation of T
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
16. Let T:P4 → P3 be a transformation defined by T(f(x)) = f'(x). This transformation is A) linear and 1-to-1 B) linear and onto C) not linear D) an isomorphism
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.