Question

let each matrix in exercises 1--6 act on c2 . find the eigenvalues and a basis for each eigenspace in c 2 .

Answer 1

The eigenvectors are (1 + i)/4 and (1-i)/4.

• A matrix is an organized, rectangular grouping of real or complex integers or functions.
• The unique collection of scalars known as eigenvalues is connected to the system of linear equations. The majority of matrix equations employ it. The German term "Eigen" signifies "appropriate" or "characteristic." Therefore, the word "eigenvalue" can also be used to refer to a suitable value, a latent root, a characteristic value, or a characteristic root. The eigenvalue is a scalar that is used to alter the eigenvector, to put it simply.
• The non-zero vectors that do not change direction when a linear transformation is performed are called eigenvectors. It is only modified by a single scalar component.

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