a. Let A be a diagonalizable n × n matrix. Show that if

Chapter , Problem 8E

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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.

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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),

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