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calcule A−1A^{-1} en calcul matriciel quand A=∣−10 32∣A = \left| \begin{array}{cc} -1 & 0 \ 3 & 2 \end{array} \right|

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Q. calcule A−1A^{-1} en calcul matriciel quand A=∣−10 32∣A = \left| \begin{array}{cc} -1 & 0 \ 3 & 2 \end{array} \right|
  1. Identify Matrix A: Step 11: Identify the matrix AA and its elements.\newlineMatrix A=(−10 32)A = \begin{pmatrix} -1 & 0 \ 3 & 2 \end{pmatrix}
  2. Calculate Determinant: Step 22: Calculate the determinant of AA.\newlineDeterminant (det AA) = (−1)(2)−(0)(3)=−2(-1)(2) - (0)(3) = -2.
  3. Find Cofactor Matrix: Step 33: Find the matrix of cofactors for AA.\newlineCofactor matrix of AA = ∣20 −3−1∣\left| \begin{array}{cc} 2 & 0 \ -3 & -1 \end{array} \right|
  4. Transpose Cofactor Matrix: Step 44: Transpose the cofactor matrix to get the adjugate matrix.\newlineAdjugate matrix (adj AA) = \left|\begin{array}{cc}\(\newline\)\(2\) & \(-3\) (\newline\)\(0\) & \(-1\)\(\newline\)\end{array}\right|
  5. Calculate Inverse: Step 55: Calculate the inverse of AA using the formula A−1=1det A⋅adj AA^{-1} = \frac{1}{\text{det } A} \cdot \text{adj } A.A−1=1(−2)⋅∣2−3 0−1∣=∣−11.5 00.5∣A^{-1} = \frac{1}{(-2)} \cdot \begin{vmatrix} 2 & -3 \ 0 & -1 \end{vmatrix} = \begin{vmatrix} -1 & 1.5 \ 0 & 0.5 \end{vmatrix}

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