Solution Found!
In Example 2, solve the first equation in (2) for x2 in
Chapter 5, Problem 21E(choose chapter or problem)
In Example 2, solve the first equation in (2) for x2 in terms of x1, and from that produce the eigenvector for the matrix A. Show that this y is a (complex) multiple of the vector v1 used in Example 2.Reference: Find the eigenvalues of A, and find a basis for each eigenspace.
Questions & Answers
QUESTION:
In Example 2, solve the first equation in (2) for x2 in terms of x1, and from that produce the eigenvector for the matrix A. Show that this y is a (complex) multiple of the vector v1 used in Example 2.Reference: Find the eigenvalues of A, and find a basis for each eigenspace.
ANSWER:Solution 21EStep 1 Consider the matrix .The objective is to find eigenvector by solving the first equation for in terms of . And show that the vector is a complex multiple of the vector Find the vectors The characteristic equation of A is, Use the quadratic formula to find the eigenvalues: Therefore the eigenvalues are