Bheactoran aonaid: leudachadh

curriculum-key-fact
  • Tha meudachd de 1 aig bheactoran aonaid.

'S e na bheactoran aonaid bunaiteach \(i = \left( \begin{array}{l}1\\ 0\\0\end{array} \right)\), \(j=\left(\begin{array}{l}0\\1\\0\end{array}\right)\) agus \(k = \left(\begin{array}{l} 0\\ 0\\1\end{array} \right)\)

Faodar bheactor sam bith a sgrìobhadh ann an teirmean de \(i\), \(j\) agus \(k\). Mar eisimpleir:

\[\left(\begin{array}{l}\,\,\,\,\,\,3\\\,\,\,\,\,4\\- 2\end{array} \right) = \left(\begin{array}{l}\,3\\0\\0\end{array} \right) + \left(\begin{array}{l}\,0\\4\\0\end{array} \right) + \left(\begin{array}{l}\,\,\,\,\,0\\\,\,\,\,\,0\\- 2\end{array} \right)\]

\[= 3\left(\begin{array}{l}1\\0\\0\end{array} \right) + 4\left( \begin{array}{l}0\\1\\0\end{array} \right) - 2\left( \begin{array}{l}0\\0\\1\end{array} \right)\]

\[= 3i + 4j - 2k\]

Question

Sgrìobh \(\left( \begin{array}{l} \,\,\,\,\,5\\\,\,\,\,\,0\\ - 1\end{array} \right)\) ann an teirmean de bheactoran aonaid.

\[\left( \begin{array}{l} \,\,\,\,\,5\\\,\,\,\,\,0\\ - 1\end{array} \right) = 5i + 0j - 1k\]

\[= 5i - k\]