मान लीजिए A = left[ {begin{array}{*{20}{c}}1& | vedclass

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(D) दिया गया है $A = \left[ {\begin{array}{*{20}{c}}1&0&0\2&1&0\3&2&1\end{array}} ight]$,$A{u_1} = \left[ {\begin{array}{*{20}{c}}1\0\0\end{arra

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$\left[ {\begin{array}{*{20}{c}}1\{ - 1}\{ - 1}\end{array}} ight]$

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(D) दिया गया है $A = \left[ {\begin{array}{*{20}{c}}1&0&0\2&1&0\3&2&1\end{array}} ight]$,$A{u_1} = \left[ {\begin{array}{*{20}{c}}1\0\0\end{array}} ight]$,और $A{u_2} = \left[ {\begin{array}{*{20}{c}}0\1\0\end{array}} ight]$।दोनों समीकरणों को जोड़ने पर,हमें प्राप्त होता है:$A{u_1} + A{u_2} = \left[ {\begin{array}{*{20}{c}}1\0\0\end{array}} ight] + \left[ {\begin{array}{*{20}{c}}0\1\0\end{array}} ight]$$A(u_1 + u_2) = \left[ {\begin{array}{*{20}{c}}1\1\0\end{array}} ight]$अतः,$u_1 + u_2 = A^{-1} \left[ {\begin{array}{*{20}{c}}1\1\0\end{array}} ight]$।सबसे पहले,$|A| = 1(1-0) - 0 + 0 = 1$ ज्ञात करें।इसके बाद,$adj(A)$ ज्ञात करें। सहखंड (cofactors) इस प्रकार हैं:$C_{11} = 1, C_{12} = -2, C_{13} = 1$$C_{21} = 0, C_{22} = 1, C_{23} = -2$$C_{31} = 0, C_{32} = 0, C_{33} = 1$अतः,$adj(A) = \left[ {\begin{array}{*{20}{c}}1&0&0\-2&1&0\1&-2&1\end{array}} ight]$।चूंकि $|A| = 1$,इसलिए $A^{-1} = adj(A)$।$u_1 + u_2 = \left[ {\begin{array}{*{20}{c}}1&0&0\-2&1&0\1&-2&1\end{array}} ight] \left[ {\begin{array}{*{20}{c}}1\1\0\end{array}} ight] = \left[ {\begin{array}{*{20}{c}}1(1)+0(1)+0(0)\-2(1)+1(1)+0(0)\1(1)-2(1)+1(0)\end{array}} ight] = \left[ {\begin{array}{*{20}{c}}1\-1\-1\end{array}} ight]$।

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