Given the vector space (R³(R),+,.), two bases of S = {e₁,e2,e3}, eieR³, ie {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 F-049 P = 1 -2 is the transition matrix from basis S to basis S', then If, 1 -1 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1B
Given the vector space (R³(R),+,·), two bases of S = {e₁,e2,e3}, ei≤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
ƒ: R³ →R³ : (x,y,z) → ƒ (x,y,z) = (3x+2y, -x, z).
-1
-1 1
4 -1
P = 1
0
-2 1
is the transition matrix from basis S to basis S', then
If,
Find the basis S={e1,e2,e3} of R³.
Transcribed Image Text:1B Given the vector space (R³(R),+,·), two bases of S = {e₁,e2,e3}, ei≤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 ƒ: R³ →R³ : (x,y,z) → ƒ (x,y,z) = (3x+2y, -x, z). -1 -1 1 4 -1 P = 1 0 -2 1 is the transition matrix from basis S to basis S', then If, Find the basis S={e1,e2,e3} of R³.
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