A 3 x 3 matrix A satisfies 1 A 00 8-8-8-8 and A 1 0 A...

  

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A 3 x 3 matrix A satisfies 1 A 00 8-8-8-8 and A 1 0 A = (-2) = (-2) 1 0 (a) Show that A is invertible. Write the characteristic polynomial of A. (b) Is A diagonalizable? If so, determine an invertible matrix P and a diagonal matrix D such that P-¹AP = D.( (c) Determine the eigenvalues and the eigenvectors of the matrix A-¹. ( A 3 x 3 matrix A satisfies 1 A 00 8-8-8-8 and A 1 0 A = (-2) = (-2) 1 0 (a) Show that A is invertible. Write the characteristic polynomial of A. (b) Is A diagonalizable? If so, determine an invertible matrix P and a diagonal matrix D such that P-¹AP = D.( (c) Determine the eigenvalues and the eigenvectors of the matrix A-¹. (

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a A is invertible because the column vectors are linearly independent They are not multiples ... View the full answer