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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A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

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A: given that                                           f:N×N→R is defined.…

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Q: Q1. Let f: N x N R be defined by (a + 1)(a + 2b) f(a, b) – 2 Show that the image of f is contained…

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Q: = Let p¹²-2x+1, p² = 3 +3x+1 and p35x + 10. Let = x³-3x + 4. Is q in me span of pl,p2 and p3?

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Q: Consider the function ƒ (x₁, x₂ ) = 5 x² + 4 x² defined on (x₁, x2) = R². The function f (x1, x₂) is…

A: The objective of the question is to determine whether the function f(x1, x2) = 5x1^2 + 4x2^2 is…