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 $C_{21}$: $$ C_{21} ___ _____ __________ ____ __________ ________ ____ __________ ______ _____.
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सबसे पहले $A$ का सह-आव्यूह (Adjoint) ज्ञात करते हैं। दिया हुआ आव्यूह: $$ 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} ___ _____ __________ ____ __________ ________ ____ __________ ______ _____.
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Find the eigenvalues and eigenvectors of the matrix B = . Is the matrix diagonalisable? Justify your answer.
Show that W = {(x, 4x, 3x) ∈ R²x ∈ R} is a subspace of R³. Also find a basis for subspace U of R³ which satisfies W ⊕ U = R³.
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