x, consisting of a single vector with integer coordinates, whose entries are as small as possible. Find a basis for the line through the origin in R² with equation y а. b. Find a basis for the line through the origin in R2 with equation y х, = - 3 consisting of a single vector with an integer x-coordinate, whose entries are as small as possible. Repeat (b), but the vector should have an integer y-coordinate, with entries as small as possible. с. Find a basis for the plane II : 3x – 7y + 4z = 0 in R³, consisting of two vectors with integer coordinates, where one component in each vector is 0. There is more d. than one correct answer.

x, consisting of a single vector with integer coordinates, whose entries are as small as possible. Find a basis for the line through the origin in R² with equation y а. b. Find a basis for the line through the origin in R2 with equation y х, = - 3 consisting of a single vector with an integer x-coordinate, whose entries are as small as possible. Repeat (b), but the vector should have an integer y-coordinate, with entries as small as possible. с. Find a basis for the plane II : 3x – 7y + 4z = 0 in R³, consisting of two vectors with integer coordinates, where one component in each vector is 0. There is more d. than one correct answer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 22EQ

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