$X$ तथा $Y$ ज्ञात कीजिए यदि

$X+Y=\left[\begin{array}{ll}7 & 0 \\ 2 & 5\end{array}\right]$ तथा $X-Y=\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$

यदि $\left[ {\begin{array}{*{20}{c}}x&0\\1&y\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}{ – 2}&1\\3&4\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}3&5\\6&3\end{array}} \right] – \left[ {\begin{array}{*{20}{c}}2&4\\2&1\end{array}} \right]$, तो

समीकरण $\left[ {\begin{array}{*{20}{c}}1&0&1\\{ – 1}&1&0\\0&{ – 1}&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ \begin{array}{l}1\\1\\2\end{array} \right]$  का हल है, $(x,y,z)$=

$\cos \theta \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{\sin \theta }\\{ – \sin \theta }&{\cos \theta }\end{array}} \right] + \sin \theta \left[ {\begin{array}{*{20}{c}}{\sin \theta }&{ – \cos \theta }\\{\cos \theta }&{\sin \theta }\end{array}} \right] = $

यदि $[m \ n]\left[ {\begin{array}{*{20}{c}}m\\n\end{array}} \right] = [25]$ और $m< n$,  तो $(m, n) =$