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Consider the following vectors in R³: (0) V₁ √3 4 V₂ = 72 = √6 1 (a) Show that these vectors are orthonormal. (b) Explain why it is then clear that 7₁, 72, V3 is a basis for R³. (c) Compute the coordinates for the following vectors in the basis 7₁, V2, V3: -3 uz 2 In each case, confirm your solution. 1:52 = V3 - (9). () 0 0 7 (-) 2

Consider the following vectors in R³: (0) V₁ √3 4 V₂ = 72 = √6 1 (a) Show that these vectors are orthonormal. (b) Explain why it is then clear that 7₁, 72, V3 is a basis for R³. (c) Compute the coordinates for the following vectors in the basis 7₁, V2, V3: -3 uz 2 In each case, confirm your solution. 1:52 = V3 - (9). () 0 0 7 (-) 2

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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Consider the following vectors in R³: (0) V₁ √3 4 V₂ = 72 = √6 1 (a) Show that these vectors are orthonormal. (b) Explain why it is then clear that 7₁, 72, V3 is a basis for R³. (c) Compute the coordinates for the following vectors in the basis 7₁, V2, V3: -3 uz 2 In each case, confirm your solution. 1:52 = V3 - (9). () 0 0 7 (-) 2
Transcribed Image Text:Consider the following vectors in R³: (0) V₁ √3 4 V₂ = 72 = √6 1 (a) Show that these vectors are orthonormal. (b) Explain why it is then clear that 7₁, 72, V3 is a basis for R³. (c) Compute the coordinates for the following vectors in the basis 7₁, V2, V3: -3 uz 2 In each case, confirm your solution. 1:52 = V3 - (9). () 0 0 7 (-) 2
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Step 1: Determine the vectors are orthonormal.

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