If there is a non-singular matrix P such as P-1AP=D, matrix A is called a diagonalizable matrix. A, n x n square matrix is ​​diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues ​​of the matrix A.   A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) : 1 -1 -1 1 3 1 -3 1 -1   a)Write a program that calculates the eigenvalues ​​and eigenvectors of matrix A using NumPy. b)Write the program that determines whether the D matrix is ​​diagonal by calculating the D matrix, using NumPy.

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If there is a non-singular matrix P such as P-1AP=D, matrix A is called a diagonalizable matrix. A, n x n square matrix is ​​diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues ​​of the matrix A.

 

A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) :

1 -1 -1
1 3 1
-3 1

-1

 

a)Write a program that calculates the eigenvalues ​​and eigenvectors of matrix A using NumPy.

b)Write the program that determines whether the D matrix is ​​diagonal by calculating the D matrix, using NumPy.

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