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Determine the orthogonal basis by calculating w1 = w2 - [(23,5)] - < C2, w1 < C1, C₁ > [(-9,-2)] and calculating w2 Now simplify w2 and find the inner product of the vectors w1 and w2

Determine the orthogonal basis by calculating w1 = w2 - [(23,5)] - < C2, w1 < C1, C₁ > [(-9,-2)] and calculating w2 Now simplify w2 and find the inner product of the vectors w1 and w2

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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I got the top parts, but I'm not sure what is being asked in the bottom parts or how I was supposed to know. Please help. Thank you.

Let A basis of R². Write these columns as vectors. The columns are C1 -9 and C2: = 23 -217 9 23 2 5 w1 w2 -2 when written as vectors. 5 The inner product of these vectors is and < C1, C1 >² = and consider the columns of this invertible matrix as a linearly independent = Determine the orthogonal basis by calculating [(23,5)] - = 85 < C2, w₁ > < C1, C₁ [(-9,-2)] and calculating w2 Now simplify w2 and find the inner product of the vectors w1 and w2
Transcribed Image Text:Let A basis of R². Write these columns as vectors. The columns are C1 -9 and C2: = 23 -217 9 23 2 5 w1 w2 -2 when written as vectors. 5 The inner product of these vectors is and < C1, C1 >² = and consider the columns of this invertible matrix as a linearly independent = Determine the orthogonal basis by calculating [(23,5)] - = 85 < C2, w₁ > < C1, C₁ [(-9,-2)] and calculating w2 Now simplify w2 and find the inner product of the vectors w1 and w2
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