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Inverses and Systems of Equations

  • Thomas Banchoff
  • John Wermer
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

If a, x, y are numbers, then
$$ a(x\;{\rm{ + }}\;y)\;{\rm{ = }}\;ax\;{\rm{ + }}\;ay. $$
If A is a linear transformation and X and Y are vectors, then by Theorem 2.1 of Chapter 2.2,
$$ A(X\;{\rm{ + }}\;Y)\;{\rm{ = }}\;A(X)\;{\rm{ + }}\;A(Y). $$
Thus we see that the operation which takes a number x into the number ax is somehow similar to the operation which takes a vector X into the vector A(X), where A is a linear transformation.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Thomas Banchoff
    • 1
  • John Wermer
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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