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.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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