Question

Given a matrix a = [4 -3 0 0 1 0 -4 4 1], find a matrix b such that b² = a?

Answer 1

To find a matrix b such that b² = a, you can use the eigenvalue decomposition method. The matrix a can be diagonalized as a = PDP^-1, where P is the matrix of eigenvectors and D is the diagonal matrix of eigenvalues. Solve for B to get B = P^-1DP.

Step-by-step explanation:

To find a matrix b such that b² = a, we can use the eigenvalue decomposition method. The matrix a can be diagonalized as a = PDP-1, where P is the matrix of eigenvectors and D is the diagonal matrix of eigenvalues. Since b² = a, we can substitute the diagonalized form into the equation: (PBP-1)² = PDP-1, which simplifies to PB²P-1 = PD. Solving for B, we get B = P-1DP.