11. In the vector space R3 we are given the subspace Y =< (1, 1, –1), (0,-4, 5), (3,-1, 2) > . (a) Which conditions must the real numbers a, b and c satisfy in order the vector (a, b, c) lies in the subspace Y ? (b) Find a basis for Y. (c) Extend the basis you have found in (b) to a basis of the whole space R3.

11. In the vector space R3 we are given the subspace Y =< (1, 1, –1), (0,-4, 5), (3,-1, 2) > . (a) Which conditions must the real numbers a, b and c satisfy in order the vector (a, b, c) lies in the subspace Y ? (b) Find a basis for Y. (c) Extend the basis you have found in (b) to a basis of the whole space R3.

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

11. In the vector space R3 we are given the subspace
Y =< (1, 1, –1), (0,-4, 5), (3,-1, 2) > .
(a) Which conditions must the real numbers a, b and c satisfy in order
the vector (a, b, c) lies in the subspace Y ?
(b) Find a basis for Y.
(c) Extend the basis you have found in (b) to a basis of the whole space
R3.

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