Answer :
The eigenvalues of an n × n matrix a are the entries on the main diagonal of the matrix a when it is put in its diagonal form.
The diagonal form of a matrix is obtained when all its off-diagonal elements are zero.
The eigenvalues of an n × n matrix a are the scalar values associated with the linear transformation represented by the matrix. To find these eigenvalues, one needs to put the matrix a into its diagonal form. This is done by finding the eigenvectors, which are vectors that do not change direction when the linear transformation is applied. The eigenvectors form the basis for the matrix a and thus its elements are zero outside of the main diagonal. When the matrix is in its diagonal form, the eigenvalues are the entries on the main diagonal. Thus, the eigenvalues of an n × n matrix a are the entries on the main diagonal of the matrix a when it is put in its diagonal form.
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