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O Let f: R2 R³ be a linear map such that f(1,2)= (1,1,2), and f(2, 1) = (2,2,1). Then which equalitie are correct? f(0,0) = (0,0,0). f(1, 1) = (1, 1, 1). f(-1, 1) = (-1, —1, 1). O ƒ(-1, -1) = (-1, —1, 1).

O Let f: R2 R³ be a linear map such that f(1,2)= (1,1,2), and f(2, 1) = (2,2,1). Then which equalitie are correct? f(0,0) = (0,0,0). f(1, 1) = (1, 1, 1). f(-1, 1) = (-1, —1, 1). O ƒ(-1, -1) = (-1, —1, 1).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section: Chapter Questions
Problem 16RQ
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M Let f: R2 R³ be a linear map such that f(1,2)= (1, 1, 2), and f(2, 1) = (2,2,1). Then which equalitie are correct? f(0,0) = (0,0,0). f(1, 1) = (1, 1, 1). f(-1, 1) = (-1,-1, 1). f(-1,-1) = (-1,-1, 1).
Transcribed Image Text:M Let f: R2 R³ be a linear map such that f(1,2)= (1, 1, 2), and f(2, 1) = (2,2,1). Then which equalitie are correct? f(0,0) = (0,0,0). f(1, 1) = (1, 1, 1). f(-1, 1) = (-1,-1, 1). f(-1,-1) = (-1,-1, 1).
Let V and V' be vector spaces over a field F and let f: V→ V' be a linear map. Which of the following statemens are correct? f is bijective if ker f = 0. f is surjective if Imf = V'. ker f is a subspace of V. f is injective if ker f = 0.
Transcribed Image Text:Let V and V' be vector spaces over a field F and let f: V→ V' be a linear map. Which of the following statemens are correct? f is bijective if ker f = 0. f is surjective if Imf = V'. ker f is a subspace of V. f is injective if ker f = 0.
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