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.

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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Question

2.2 #1 please answer A B C and D

The problems are in the picture.

Find a basis for the line through the origin in R² with equation y =
x, consisting
а.
of a single vector with integer coordinates, whose entries are as small as possible.
b.
Find a basis for the line through the origin in R² with equation y
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
than one correct answer.
d.
-

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Step 2: Find the basis for the line passing through origin with equation y = 5/7x.

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Step 3: Find the basis for line through origin with equation y = - sqrt(2)/3x.

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