Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Using basis and dimensions in vector space section for linear algebra

78. \( W = \{(s + 4t, t, s, 2s - t) : s \text{ and } t \text{ are real numbers}\} \) This mathematical expression defines a set \( W \) consisting of ordered quadruples. Each quadruple is formed using the real numbers \( s \) and \( t \). The components of each quadruple are calculated as follows: 1. The first component is \( s + 4t \). 2. The second component is \( t \). 3. The third component is \( s \). 4. The fourth component is \( 2s - t \). By varying the values of \( s \) and \( t \), you can generate all possible quadruples within the set \( W \). This set is defined in a 4-dimensional space, originating from the linear combination of the parameters \( s \) and \( t \).
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Transcribed Image Text:78. \( W = \{(s + 4t, t, s, 2s - t) : s \text{ and } t \text{ are real numbers}\} \) This mathematical expression defines a set \( W \) consisting of ordered quadruples. Each quadruple is formed using the real numbers \( s \) and \( t \). The components of each quadruple are calculated as follows: 1. The first component is \( s + 4t \). 2. The second component is \( t \). 3. The third component is \( s \). 4. The fourth component is \( 2s - t \). By varying the values of \( s \) and \( t \), you can generate all possible quadruples within the set \( W \). This set is defined in a 4-dimensional space, originating from the linear combination of the parameters \( s \) and \( t \).
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