A=[(2,3),(1,4)] হলে Adj(A) = কোনটি?

Another Explanation (5):

সমাধান:

প্রথমে আমরা ম্যাট্রিক্স \(A\) কে দেখবো:

\[A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}\]

\[ \det(A) = (2)(4) - (3)(1) = 8 - 3 = 5 \]

\[ \text{cof}(A) = \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix} \]

\( C_{11} = (+1)^{1+1} \times \det \begin{bmatrix} 4 \end{bmatrix} = 1 \times 4 = 4 \)
\( C_{12} = (+1)^{1+2} \times \det \begin{bmatrix} 1 \end{bmatrix} = -1 \times 1 = -1 \)
\( C_{21} = (+1)^{2+1} \times \det \begin{bmatrix} 3 \end{bmatrix} = -1 \times 3 = -3 \)
\( C_{22} = (+1)^{2+2} \times \det \begin{bmatrix} 2 \end{bmatrix} = 1 \times 2 = 2 \)

\[ \text{cof}(A) = \begin{bmatrix} 4 & -1 \\ -3 & 2 \end{bmatrix} \]

\[ \text{adj}(A) = \text{cof}(A)^T = \begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix} \]

অতএব, adj}(A) = \begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}