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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78. W = {(s + 4t, t, s, 2s — t): s and t are real numbers}

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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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 \( t \).

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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