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Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the space R^4

Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the space R^4

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the space R^4?

 

(a) {(1,1,1,-1)}. (b) {(1,-1,0,0), (1, 0, 0, 1), (0, 1, 0, 1)}. (c) {(2,2,0,-2), (0,0,1,0)}. (d) {(1,0,0,0), (0, 1, 0, 0), (0, 0, 1, 0)}. (e) {(1, 1, 0, 0), (0, 1, 1, 0), (0, 0, 1, 1), (0, 0, 0, 1)}.
Transcribed Image Text:(a) {(1,1,1,-1)}. (b) {(1,-1,0,0), (1, 0, 0, 1), (0, 1, 0, 1)}. (c) {(2,2,0,-2), (0,0,1,0)}. (d) {(1,0,0,0), (0, 1, 0, 0), (0, 0, 1, 0)}. (e) {(1, 1, 0, 0), (0, 1, 1, 0), (0, 0, 1, 1), (0, 0, 0, 1)}.
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