Let f: R2 R2 be defined f(x, y) = (3x + y,x+y). (a) Prove that f is a bijection. (b) Keep f the same but change its domain and codomain to Z². Is f still a bijection?

Elementary Linear Algebra (MindTap Course List)
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
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5. Let f: R² R2 be defined f(x, y) = (3x + y, x+y).
(a) Prove that f is a bijection.
(b) Keep f the same but change its domain and codomain to Z². Is f still a bijection?
Transcribed Image Text:5. Let f: R² R2 be defined f(x, y) = (3x + y, x+y). (a) Prove that f is a bijection. (b) Keep f the same but change its domain and codomain to Z². Is f still a bijection?
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