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Consider the ordered bases B₁ = {(−1, 1, 0), (0, 1, 1), (1, 0, 0)} of R³ and B₂ = {(1, 2), (1, −1)} of R². (a) Let f: R³ → R² be the linear transformation such that m(f) B₁, B2 Find g(2,-1,3). = 12 1 1 Find f(2, 1,-1). (b) Let g: R³ → R² be the linear transformation such that 3. g(-1,1,0) = (1, 0) g(0, 1, 1) = (0, -2) g(1,0,0) = (–1,1).

Consider the ordered bases B₁ = {(−1, 1, 0), (0, 1, 1), (1, 0, 0)} of R³ and B₂ = {(1, 2), (1, −1)} of R². (a) Let f: R³ → R² be the linear transformation such that m(f) B₁, B2 Find g(2,-1,3). = 12 1 1 Find f(2, 1,-1). (b) Let g: R³ → R² be the linear transformation such that 3. g(-1,1,0) = (1, 0) g(0, 1, 1) = (0, -2) g(1,0,0) = (–1,1).

Advanced Engineering Mathematics
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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Consider the ordered bases B₁ = {(-1, 1, 0), (0, 1, 1), (1, 0, 0)} of R³ and B₂ = {(1,2), (1, −1)} of R². (a) Let f: R³ → R² be the linear transformation such that m(f) B₁,B2 Find g(2,-1,3). = 1 2 1 1 1 Find f(2, 1,-1). (b) Let g: R³ → R² be the linear transformation such that g(-1,1,0) = (1, 0) g(0, 1, 1) = (0, -2) g(1,0,0) = (-1, 1).
Transcribed Image Text:Consider the ordered bases B₁ = {(-1, 1, 0), (0, 1, 1), (1, 0, 0)} of R³ and B₂ = {(1,2), (1, −1)} of R². (a) Let f: R³ → R² be the linear transformation such that m(f) B₁,B2 Find g(2,-1,3). = 1 2 1 1 1 Find f(2, 1,-1). (b) Let g: R³ → R² be the linear transformation such that g(-1,1,0) = (1, 0) g(0, 1, 1) = (0, -2) g(1,0,0) = (-1, 1).
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