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Determine whether each of the sets below is a basis for R³. Explain any theorems or results you rely on in your answers. (a) X = {(1, 1, 1), (1, −1, 1), (1, 1, −1)}. (b) Y = {(1, −2, −1), (2, −3, 1), (5, —8, 1)}. (c) Z = {(1, 0, 1). 0), (0,3,3)}.

Determine whether each of the sets below is a basis for R³. Explain any theorems or results you rely on in your answers. (a) X = {(1, 1, 1), (1, −1, 1), (1, 1, −1)}. (b) Y = {(1, −2, −1), (2, −3, 1), (5, —8, 1)}. (c) Z = {(1, 0, 1). 0), (0,3,3)}.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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10. Determine whether each of the sets below is a basis for R³. Explain any theorems or results you rely on in your answers. (a) X = {(1, 1, 1), (1, −1, 1), (1, 1, -1)}. (b) Y = {(1, -2, −1), (2, −3, 1), (5, −8, 1)}. (c) Z = {(1, 0, 1), (2, 2, 0), (0, 3, 3)}.
Transcribed Image Text:10. Determine whether each of the sets below is a basis for R³. Explain any theorems or results you rely on in your answers. (a) X = {(1, 1, 1), (1, −1, 1), (1, 1, -1)}. (b) Y = {(1, -2, −1), (2, −3, 1), (5, −8, 1)}. (c) Z = {(1, 0, 1), (2, 2, 0), (0, 3, 3)}.
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