- Calcule as matrizes inversas das 4 matrizes abaixo. 4) \( A=\left[\begin{array}{ll}3 & 5 \\ 1 & 2\end{array}\right] \) 5) \( \mathrm{B}=\left[\begin{array}{rrr}-3 & 4 & -5 \\ 0 & 1 & 2 \\ 3 & -5 & 4\end{array}\right] \) 6) \( C=\left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 3 & 2 & 1 & 0 \\ 4 & 3 & 2 & 1\end{array}\right] \) 7) \( \mathrm{D}=\left[\begin{array}{rrr}1 & 0 & -2 \\ -3 & -2 & -2 \\ -3 & 0 & 2\end{array}\right] \)

Matrices by following steps: - step0: Find the matrix inverse: \(\left[\begin{array}{ll}{3}&{5}\\{1}&{2}\end{array}\right]\) - step1: Evaluate the determinant: \(1\) - step2: Using the formula: \(\frac{1}{3\times 2-5\times 1}\times \left[\begin{array}{ll}{2}&{-5}\\{-1}&{3}\end{array}\right]\) - step3: Evaluate: \(1\times \left[\begin{array}{ll}{2}&{-5}\\{-1}&{3}\end{array}\right]\) - step4: Calculate the product: \(\left[\begin{array}{ll}{2}&{-5}\\{-1}&{3}\end{array}\right]\) Find the inverse matrix of \( \left[\begin{array}{rrr}-3 & 4 & -5 \\ 0 & 1 & 2 \\ 3 & -5 & 4\end{array}\right] \). Matrices by following steps: - step0: Find the matrix inverse: \(\left[\begin{array}{lll}{-3}&{4}&{-5}\\{0}&{1}&{2}\\{3}&{-5}&{4}\end{array}\right]\) - step1: Begin by adjoining the identity matrix to form the matrix: \(\left[\begin{array}{lll|lll}{-3}&{4}&{-5}&{1}&{0}&{0}\\{0}&{1}&{2}&{0}&{1}&{0}\\{3}&{-5}&{4}&{0}&{0}&{1}\end{array}\right]\) - step2: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{-\frac{4}{3}}&{\frac{5}{3}}&{-\frac{1}{3}}&{0}&{0}\\{0}&{1}&{2}&{0}&{1}&{0}\\{3}&{-5}&{4}&{0}&{0}&{1}\end{array}\right]\) - step3: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{-\frac{4}{3}}&{\frac{5}{3}}&{-\frac{1}{3}}&{0}&{0}\\{0}&{1}&{2}&{0}&{1}&{0}\\{0}&{-1}&{-1}&{1}&{0}&{1}\end{array}\right]\) - step4: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{-\frac{4}{3}}&{\frac{5}{3}}&{-\frac{1}{3}}&{0}&{0}\\{0}&{1}&{2}&{0}&{1}&{0}\\{0}&{0}&{1}&{1}&{1}&{1}\end{array}\right]\) - step5: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{-\frac{4}{3}}&{\frac{5}{3}}&{-\frac{1}{3}}&{0}&{0}\\{0}&{1}&{0}&{-2}&{-1}&{-2}\\{0}&{0}&{1}&{1}&{1}&{1}\end{array}\right]\) - step6: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{-\frac{4}{3}}&{0}&{-2}&{-\frac{5}{3}}&{-\frac{5}{3}}\\{0}&{1}&{0}&{-2}&{-1}&{-2}\\{0}&{0}&{1}&{1}&{1}&{1}\end{array}\right]\) - step7: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{0}&{0}&{-\frac{14}{3}}&{-3}&{-\frac{13}{3}}\\{0}&{1}&{0}&{-2}&{-1}&{-2}\\{0}&{0}&{1}&{1}&{1}&{1}\end{array}\right]\) - step8: Write the right half matrix: \(\left[\begin{array}{lll}{-\frac{14}{3}}&{-3}&{-\frac{13}{3}}\\{-2}&{-1}&{-2}\\{1}&{1}&{1}\end{array}\right]\) Find the inverse matrix of \( \left[\begin{array}{rrr}1 & 0 & -2 \\ -3 & -2 & -2 \\ -3 & 0 & 2\end{array}\right] \). Matrices by following steps: - step0: Find the matrix inverse: \(\left[\begin{array}{lll}{1}&{0}&{-2}\\{-3}&{-2}&{-2}\\{-3}&{0}&{2}\end{array}\right]\) - step1: Begin by adjoining the identity matrix to form the matrix: \(\left[\begin{array}{lll|lll}{1}&{0}&{-2}&{1}&{0}&{0}\\{-3}&{-2}&{-2}&{0}&{1}&{0}\\{-3}&{0}&{2}&{0}&{0}&{1}\end{array}\right]\) - step2: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{0}&{-2}&{1}&{0}&{0}\\{0}&{-2}&{-8}&{3}&{1}&{0}\\{-3}&{0}&{2}&{0}&{0}&{1}\end{array}\right]\) - step3: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{0}&{-2}&{1}&{0}&{0}\\{0}&{-2}&{-8}&{3}&{1}&{0}\\{0}&{0}&{-4}&{3}&{0}&{1}\end{array}\right]\) - step4: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{0}&{-2}&{1}&{0}&{0}\\{0}&{1}&{4}&{-\frac{3}{2}}&{-\frac{1}{2}}&{0}\\{0}&{0}&{-4}&{3}&{0}&{1}\end{array}\right]\) - step5: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{0}&{-2}&{1}&{0}&{0}\\{0}&{1}&{4}&{-\frac{3}{2}}&{-\frac{1}{2}}&{0}\\{0}&{0}&{1}&{-\frac{3}{4}}&{0}&{-\frac{1}{4}}\end{array}\right]\) - step6: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{0}&{-2}&{1}&{0}&{0}\\{0}&{1}&{0}&{\frac{3}{2}}&{-\frac{1}{2}}&{1}\\{0}&{0}&{1}&{-\frac{3}{4}}&{0}&{-\frac{1}{4}}\end{array}\right]\) - step7: Simplify the row: \(\left[\begin{array}{lll|lll}{1}&{0}&{0}&{-\frac{1}{2}}&{0}&{-\frac{1}{2}}\\{0}&{1}&{0}&{\frac{3}{2}}&{-\frac{1}{2}}&{1}\\{0}&{0}&{1}&{-\frac{3}{4}}&{0}&{-\frac{1}{4}}\end{array}\right]\) - step8: Write the right half matrix: \(\left[\begin{array}{lll}{-\frac{1}{2}}&{0}&{-\frac{1}{2}}\\{\frac{3}{2}}&{-\frac{1}{2}}&{1}\\{-\frac{3}{4}}&{0}&{-\frac{1}{4}}\end{array}\right]\) Find the inverse matrix of \( \left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 3 & 2 & 1 & 0 \\ 4 & 3 & 2 & 1\end{array}\right] \). Matrices by following steps: - step0: Find the matrix inverse: \(\left[\begin{array}{llll}{1}&{0}&{0}&{0}\\{2}&{1}&{0}&{0}\\{3}&{2}&{1}&{0}\\{4}&{3}&{2}&{1}\end{array}\right]\) - step1: Begin by adjoining the identity matrix to form the matrix: \(\left[\begin{array}{llll|llll}{1}&{0}&{0}&{0}&{1}&{0}&{0}&{0}\\{2}&{1}&{0}&{0}&{0}&{1}&{0}&{0}\\{3}&{2}&{1}&{0}&{0}&{0}&{1}&{0}\\{4}&{3}&{2}&{1}&{0}&{0}&{0}&{1}\end{array}\right]\) - step2: Simplify the row: \(\left[\begin{array}{llll|llll}{1}&{0}&{0}&{0}&{1}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}&{-2}&{1}&{0}&{0}\\{3}&{2}&{1}&{0}&{0}&{0}&{1}&{0}\\{4}&{3}&{2}&{1}&{0}&{0}&{0}&{1}\end{array}\right]\) - step3: Simplify the row: \(\left[\begin{array}{llll|llll}{1}&{0}&{0}&{0}&{1}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}&{-2}&{1}&{0}&{0}\\{0}&{2}&{1}&{0}&{-3}&{0}&{1}&{0}\\{4}&{3}&{2}&{1}&{0}&{0}&{0}&{1}\end{array}\right]\) - step4: Simplify the row: \(\left[\begin{array}{llll|llll}{1}&{0}&{0}&{0}&{1}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}&{-2}&{1}&{0}&{0}\\{0}&{2}&{1}&{0}&{-3}&{0}&{1}&{0}\\{0}&{3}&{2}&{1}&{-4}&{0}&{0}&{1}\end{array}\right]\) - step5: Simplify the row: \(\left[\begin{array}{llll|llll}{1}&{0}&{0}&{0}&{1}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}&{-2}&{1}&{0}&{0}\\{0}&{0}&{1}&{0}&{1}&{-2}&{1}&{0}\\{0}&{3}&{2}&{1}&{-4}&{0}&{0}&{1}\end{array}\right]\) - step6: Simplify the row: \(\left[\begin{array}{llll|llll}{1}&{0}&{0}&{0}&{1}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}&{-2}&{1}&{0}&{0}\\{0}&{0}&{1}&{0}&{1}&{-2}&{1}&{0}\\{0}&{0}&{2}&{1}&{2}&{-3}&{0}&{1}\end{array}\right]\) - step7: Simplify the row: \(\left[\begin{array}{llll|llll}{1}&{0}&{0}&{0}&{1}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}&{-2}&{1}&{0}&{0}\\{0}&{0}&{1}&{0}&{1}&{-2}&{1}&{0}\\{0}&{0}&{0}&{1}&{0}&{1}&{-2}&{1}\end{array}\right]\) - step8: Write the right half matrix: \(\left[\begin{array}{llll}{1}&{0}&{0}&{0}\\{-2}&{1}&{0}&{0}\\{1}&{-2}&{1}&{0}\\{0}&{1}&{-2}&{1}\end{array}\right]\) Aqui estão as matrizes inversas das quatro matrizes fornecidas: 4) A inversa da matriz \( A = \left[\begin{array}{ll}3 & 5 \\ 1 & 2\end{array}\right] \) é: \[ A^{-1} = \left[\begin{array}{ll}2 & -5 \\ -1 & 3\end{array}\right] \] 5) A inversa da matriz \( B = \left[\begin{array}{rrr}-3 & 4 & -5 \\ 0 & 1 & 2 \\ 3 & -5 & 4\end{array}\right] \) é: \[ B^{-1} = \left[\begin{array}{lll}-\frac{14}{3} & -3 & -\frac{13}{3} \\ -2 & -1 & -2 \\ 1 & 1 & 1\end{array}\right] \] 6) A inversa da matriz \( C = \left[\begin{array}{llll}1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 3 & 2 & 1 & 0 \\ 4 & 3 & 2 & 1\end{array}\right] \) é: \[ C^{-1} = \left[\begin{array}{llll}1 & 0 & 0 & 0 \\ -2 & 1 & 0 & 0 \\ 1 & -2 & 1 & 0 \\ 0 & 1 & -2 & 1\end{array}\right] \] 7) A inversa da matriz \( D = \left[\begin{array}{rrr}1 & 0 & -2 \\ -3 & -2 & -2 \\ -3 & 0 & 2\end{array}\right] \) é: \[ D^{-1} = \left[\begin{array}{lll}-\frac{1}{2} & 0 & -\frac{1}{2} \\ \frac{3}{2} & -\frac{1}{2} & 1 \\ -\frac{3}{4} & 0 & -\frac{1}{4}\end{array}\right] \]