Solution Found!
a. Let A be a diagonalizable n × n matrix. Show that if
Chapter , Problem 8E(choose chapter or problem)
QUESTION:
a. Let A be a diagonalizable \(n \times n\) matrix. Show that if the multiplicity of an eigenvalue \(\lambda\) is n, then \(A=\lambda I\).
b. Use part (a) to show that the matrix \(A=\left[\begin{array}{ll}3 & 1 \\ 0 & 3\end{array}\right]\) is not diagonalizable.
Questions & Answers
QUESTION:
a. Let A be a diagonalizable \(n \times n\) matrix. Show that if the multiplicity of an eigenvalue \(\lambda\) is n, then \(A=\lambda I\).
b. Use part (a) to show that the matrix \(A=\left[\begin{array}{ll}3 & 1 \\ 0 & 3\end{array}\right]\) is not diagonalizable.
ANSWER:Solution 8E(a)(b),