(See Steps) For the matrix A=[ccc5 4 2 , 2 6 -1 , 1 -3 1] Find the adjoint matrix: adj; A Compute det;(A) Verify Theorem 3.12 (pg. 167): A(adj; A)=(adj;


Question: For the matrix \(A=\left[\begin{array}{ccc}5 & 4 & 2 \\ 2 & 6 & -1 \\ 1 & -3 & 1\end{array}\right]\)

  1. Find the adjoint matrix: \(\operatorname{adj} A\)
  2. Compute \(\operatorname{det}(A)\)
  3. Verify Theorem 3.12 (pg. 167): \(A(\operatorname{adj} A)=(\operatorname{adj} A) A=\operatorname{det}(A) \mathrm{I}_{3}\)
  4. Verify Corollary \(3.4(\) pg. 168 \(): A^{-1}=\frac{1}{\operatorname{det}(A)} \operatorname{adj}(A)\)

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