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4. Recall that a basis for a vector space V is a set of vectors which are linearly independent and span V. Consider the vectors a. V1 = b. 1 3 V2 = 4 Show this set forms a basis for R³ via the following: 2 V3 = -2 2 Verify that the vectors V₁, V2, V3 are linearly independent. Show all work. Show that the vectors V₁, V2, V3 span all of R3 by showing that the following system a a is consistent for any vector b: xv₁+yv₂+ZV3 = b Fully justify your answer. Note: We are asking you to directly verify this set spans all of R³.

4. Recall that a basis for a vector space V is a set of vectors which are linearly independent and span V. Consider the vectors a. V1 = b. 1 3 V2 = 4 Show this set forms a basis for R³ via the following: 2 V3 = -2 2 Verify that the vectors V₁, V2, V3 are linearly independent. Show all work. Show that the vectors V₁, V2, V3 span all of R3 by showing that the following system a a is consistent for any vector b: xv₁+yv₂+ZV3 = b Fully justify your answer. Note: We are asking you to directly verify this set spans all of R³.

Advanced Engineering Mathematics
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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4. Recall that a basis for a vector space V is a set of vectors which are linearly independent and span V. Consider the vectors a. V1 = b. 1 -2 is consistent for any vector 3 , V2 Show this set forms a basis for R3 via the following: = 4 2 2 V3 = -2 2 Verify that the vectors V₁, V2, V3 are linearly independent. Show all work. Show that the vectors V₁, V2, V3 span all of R³ by showing that the following system a a [3] -- b: xv₁+yv2+ZV3: b. Fully justify your answer. C с Note: We are asking you to directly verify this set spans all of R³.
Transcribed Image Text:4. Recall that a basis for a vector space V is a set of vectors which are linearly independent and span V. Consider the vectors a. V1 = b. 1 -2 is consistent for any vector 3 , V2 Show this set forms a basis for R3 via the following: = 4 2 2 V3 = -2 2 Verify that the vectors V₁, V2, V3 are linearly independent. Show all work. Show that the vectors V₁, V2, V3 span all of R³ by showing that the following system a a [3] -- b: xv₁+yv2+ZV3: b. Fully justify your answer. C с Note: We are asking you to directly verify this set spans all of R³.
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