Find a basis for each of these subspaces of R4: (a) All vectors whose components are equal. (b) All vectors whose components add to zero. (c) All vectors that are perpendicular to (1,1,0,0) and (1,0,1,1). (d) The column space and the nullspace of I (4 by 4).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 32E
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Find a basis for each of these subspaces of R4:
(a) All vectors whose components are equal.
(b) All vectors whose components add to zero.
(c) All vectors that are perpendicular to (1,1,0,0) and (1,0, 1, 1).
(d) The column space and the nullspace of I (4 by 4).
Transcribed Image Text:Find a basis for each of these subspaces of R4: (a) All vectors whose components are equal. (b) All vectors whose components add to zero. (c) All vectors that are perpendicular to (1,1,0,0) and (1,0, 1, 1). (d) The column space and the nullspace of I (4 by 4).
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