Linear Combination

In <a href="https://en.wikipedia.org/wiki/Mathematics" title="Mathematics" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">mathematics</a>, a <span style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: 700; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">linear combination is an <a href="https://en.wikipedia.org/wiki/Expression(mathematics)" title="Expression (mathematics)" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">expression</a> constructed from a <a href="https://en.wikipedia.org/wiki/Set(mathematics)" title="Set (mathematics)" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">set</a> of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of <i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">x and <i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">y would be any expression of the form <i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">ax + <i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">by, where <i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">a and <i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">b are constants).<span class="mw-ref" id="cite_ref-1" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; font-size: 0.75em; line-height: 1; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: super; unicode-bidi: embed;"><a href="https://en.wikipedia.org/#cite_note-1" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161); counter-reset: mw-Ref 1;"></a><span class="mw-ref" id="cite_ref-2" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; font-size: 0.75em; line-height: 1; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: super; unicode-bidi: embed;"><a href="https://en.wikipedia.org/#cite_note-2" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161); counter-reset: mw-Ref 2;"></a><span class="mw-ref" id="cite_ref-3" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; font-size: 0.75em; line-height: 1; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: super; unicode-bidi: embed;"><a href="https://en.wikipedia.org/#cite_note-3" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161); counter-reset: mw-Ref 3;"></a> The concept of linear combinations is central to <a href="https://en.wikipedia.org/wiki/Linear_algebra" title="Linear algebra" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">linear algebra</a> and related fields of mathematics. Most of this article deals with linear combinations in the context of a <a href="https://en.wikipedia.org/wiki/Vector_space" title="Vector space" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">vector space</a> over a <a href="https://en.wikipedia.org/wiki/Field_(mathematics)" title="Field (mathematics)" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">field</a>, with some generalizations given at the end of the article.