Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

linear 3.4 Q5 sub a 

*5. Give a basis for the orthogonal complement of each of the following subspaces of \( \mathbb{R}^4 \). a. \( V = \text{Span} \left( (1, 0, 3, 4), (0, 1, 2, -5) \right) \) b. \( W = \{ x \in \mathbb{R}^4 : x_1 + 3x_3 + 4x_4 = 0, \quad x_2 + 2x_3 - 5x_4 = 0 \} \)
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Transcribed Image Text:*5. Give a basis for the orthogonal complement of each of the following subspaces of \( \mathbb{R}^4 \). a. \( V = \text{Span} \left( (1, 0, 3, 4), (0, 1, 2, -5) \right) \) b. \( W = \{ x \in \mathbb{R}^4 : x_1 + 3x_3 + 4x_4 = 0, \quad x_2 + 2x_3 - 5x_4 = 0 \} \)
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