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The Solution of a System of Equations: the Regular Case

  • P. M. Cohn
Chapter
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Part of the Library of Mathematics book series (LIMA)

Abstract

With the help of vector notation any m × n system may be written as a single vector equation. E.g. the 2x2 system
$$ \begin{array}{*{20}c} {3x + 2y = 7} \hfill \\ {2x + 5y = 12,} \hfill \\ \end{array} $$
considered in the Introduction, may be written as
$$ \left( {\begin{array}{*{20}c} 3 \\ 2 \\ \end{array} } \right)x + \left( {\begin{array}{*{20}c} 2 \\ 5 \\ \end{array} } \right)y = \left( {\begin{array}{*{20}c} 7 \\ {12} \\ \end{array} } \right), $$
where the vectors have been written as columns, instead of rows as in ch. I. This way of writing the equations puts the problem in a different light. To solve this vector equation is to express the vector on the right as a linear combination of the two vectors on the left.

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© P. M. Cohn 1958

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  • P. M. Cohn

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