1A Given the vector space (R³(R),+,-), two bases of S ={e1,e2,e3}, ei=R³, i= {1,2,3}, S'={u₁,12,U3}, where, u₁=(-1,0,1), u2=(1,1,1), u3=(0,1,-1) and the linear transformation f: R³ R³: (x,y,z) →ƒ(x,y,z) = (3x+2y, -x, z). -1 -1 1 --639 1 4 -1 0 -2 is the transition matrix from basis S to basis S', then Compute the representation matrix [f]s,off with respect to the basis S of R³, such that the matrices [f]s and [f]s' are equal. If, P = 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1A
Given the vector space (R³(R),+,·), two bases of S ={e₁,e2,e3}, e¡¤R³, i={1,2,3},
S'={u₁,u2,u3}, where, u₁=(-1,0,1), u2=(1,1,1), u3=(0,1,-1) and the linear transformation
f: R³ R³: (x,y,z) →f(x,y,z) = (3x+2y, -x, z).
-1 1
-1
4
0 -2 1
is the transition matrix from basis S to basis S', then
Compute the representation matrix [f]s,off with respect to the basis S of R³, such
that the matrices [f]s and [f]s' are equal.
If,
P = 1
Transcribed Image Text:1A Given the vector space (R³(R),+,·), two bases of S ={e₁,e2,e3}, e¡¤R³, i={1,2,3}, S'={u₁,u2,u3}, where, u₁=(-1,0,1), u2=(1,1,1), u3=(0,1,-1) and the linear transformation f: R³ R³: (x,y,z) →f(x,y,z) = (3x+2y, -x, z). -1 1 -1 4 0 -2 1 is the transition matrix from basis S to basis S', then Compute the representation matrix [f]s,off with respect to the basis S of R³, such that the matrices [f]s and [f]s' are equal. If, P = 1
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