Let E= te, ez.es} be the standard basis for R', letB= (b. b, b,) be a basis for a vector space V, and letT:R' - V be a lincar transformation with the property thatT(x. Ka. Ka) = (2x, – xa)b, – (2x3)b, + (x, + 3x, )b,a. Compute T(e,). T (e:), and T(e,).b. Compute (T(s, )]s. [T(6,)]|s, and (T(e)g.e. Find the matrix for T relative to E and B.Let B = {b. b. b, be a basis for a vector space V and letT:V - R' be a lincar transformation with the property that= [2x - 3r2 +-2r, + 5x,T(x,b, + x;b; + x,b,)Find the matrix for T relative to B and the standard basis forR.

Given: Tx1,x2,x3=2x3-x2b1-2x3b2+x1+3x2b3 a. Te1=T1,0,0=0b1+0b2+1b3 Te2=T0,1,0=-1b1+0b2+3b3…

Let E= te, e, e be the standard basis for R', let B= (b, bz. b, be a basis for a vector space V. and let T:R'- V be a lincar transformation with the property that T(x.. Ka. Xa) = (2x, - x)b, – (2x5)b; + (x, + 3x, )b, a. Compute T(e,). T (e:), and T(e,). b. Compute (T(s, )ls. [T(s;)]g, and (T(s,)]s. e. Find the matrix for T relative to E and B. Let B = {b. b. b, be a basis for a vector space V and let T:V - R' be a lincar transformation with the property that 2x -3x +x T(x,b, + x,b; +x,b,) = -2x, + 5x, Find the matrix for T relative to B and the standard basis for R.

Let E= te, e, e be the standard basis for R', let B= (b, bz. b, be a basis for a vector space V. and let T:R'- V be a lincar transformation with the property that T(x.. Ka. Xa) = (2x, - x)b, – (2x5)b; + (x, + 3x, )b, a. Compute T(e,). T (e:), and T(e,). b. Compute (T(s, )ls. [T(s;)]g, and (T(s,)]s. e. Find the matrix for T relative to E and B. Let B = {b. b. b, be a basis for a vector space V and let T:V - R' be a lincar transformation with the property that 2x -3x +x T(x,b, + x,b; +x,b,) = -2x, + 5x, Find the matrix for T relative to B and the standard basis for R.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let E= te, ez.es} be the standard basis for R', let
B= (b. b, b,) be a basis for a vector space V, and let
T:R' - V be a lincar transformation with the property that
T(x. Ka. Ka) = (2x, – xa)b, – (2x3)b, + (x, + 3x, )b,
a. Compute T(e,). T (e:), and T(e,).
b. Compute (T(s, )]s. [T(6,)]|s, and (T(e)g.
e. Find the matrix for T relative to E and B.
Let B = {b. b. b, be a basis for a vector space V and let
T:V - R' be a lincar transformation with the property that
= [2x - 3r2 +
-2r, + 5x,
T(x,b, + x;b; + x,b,)
Find the matrix for T relative to B and the standard basis for
R.

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