Question
Adj(A) ज्ञात कीजिये, जहाँ इस से A-1 निकालिये।
4) a) निम्नलिखित समीकरण निकाय को क्रमर नियम से हल कीजिये:
Answer :
Word Count : 693
सबसे पहले $A$ का सह-आव्यूह (Adjoint) ज्ञात करते हैं। दिया हुआ आव्यूह: $$ A = \begin{bmatrix} 3 & 2 & 2 \\ -1 & 1 & 0 \\ 3 & 0 & 1 \end{bmatrix} $$ ### चरण 1: सह-आव्यूह (Adjoint) के लिए कोफ़ैक्टर मैट्रिक्स निकालें #### कोफ़ैक्टर $C_{11}$: $$ C_{11} = \begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} = (1)(1) - (0)(0) = 1 $$ #### कोफ़ैक्टर $C_{12}$: $$ C_{12} = -\begin{vmatrix}-1 & 0 \\ 3 & 1\end{vmatrix} = -((-1)(1) - (0)(3)) = -(-1 -0) = 1 $$ #### कोफ़ैक्टर $C_{13}$: $$ C_{13} = \begin{vmatrix}-1 & 1 \\ 3 & 0\end{vmatrix} = (-1)(0) - (1)(3) = -3 $$ #### कोफ़ैक्टर $C_{21}$: $$ C_{21} = -\begin{vmatrix}2 & 2 \\ 0 & 1\end{vmatrix} = -((2)(1)-(2)(0)) = -(2-0) = -2 $$ #### कोफ़ैक्टर $C_{22}$: $$ C_{22} = \begin{vmatrix}3 & _______ ____ ______ _________ __________ ___ ____ ___ ______.
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सबसे पहले $A$ का सह-आव्यूह (Adjoint) ज्ञात करते हैं। दिया हुआ आव्यूह: $$ A = \begin{bmatrix} 3 & 2 & 2 \\ -1 & 1 & 0 \\ 3 & 0 & 1 \end{bmatrix} $$ ### चरण 1: सह-आव्यूह (Adjoint) के लिए कोफ़ैक्टर मैट्रिक्स निकालें #### कोफ़ैक्टर $C_{11}$: $$ C_{11} = \begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} = (1)(1) - (0)(0) = 1 $$ #### कोफ़ैक्टर $C_{12}$: $$ C_{12} = -\begin{vmatrix}-1 & 0 \\ 3 & 1\end{vmatrix} = -((-1)(1) - (0)(3)) = -(-1 -0) = 1 $$ #### कोफ़ैक्टर $C_{13}$: $$ C_{13} = \begin{vmatrix}-1 & 1 \\ 3 & 0\end{vmatrix} = (-1)(0) - (1)(3) = -3 $$ #### कोफ़ैक्टर $C_{21}$: $$ C_{21} = -\begin{vmatrix}2 & 2 \\ 0 & 1\end{vmatrix} = -((2)(1)-(2)(0)) = -(2-0) = -2 $$ #### कोफ़ैक्टर $C_{22}$: $$ C_{22} = \begin{vmatrix}3 & _______ ____ ______ _________ __________ ___ ____ ___ ______.
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Related Questions
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जाँच कीजिये कि की उप सम्ष्टि है या नहीं।
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