Linear Equations pp 14-26 | Cite as

# The Solution of a System of Equations: the Regular Case

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## Abstract

With the help of vector notation any
considered in the Introduction, may be written as
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.

*m*×*n*system may be written as a single vector equation. E.g. the 2x2 system$$
\begin{array}{*{20}c}
{3x + 2y = 7} \hfill \\
{2x + 5y = 12,} \hfill \\
\end{array}
$$

$$
\left( {\begin{array}{*{20}c}
3 \\
2 \\
\end{array} } \right)x + \left( {\begin{array}{*{20}c}
2 \\
5 \\
\end{array} } \right)y = \left( {\begin{array}{*{20}c}
7 \\
{12} \\
\end{array} } \right),
$$

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## Copyright information

© P. M. Cohn 1958