Solution Found!
Decide (as efficiently as possible) which of the following matrices are diagonalizable
Chapter 6, Problem 5(choose chapter or problem)
Decide (as efficiently as possible) which of the following matrices are diagonalizable. Give your reasoning.
\(\begin{array}{l} A=\left[\begin{array}{lll} 5 & 0 & 2 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{array}\right], \quad B=\left[\begin{array}{lll} 5 & 0 & 2 \\ 0 & 5 & 0 \\ 2 & 0 & 5 \end{array}\right]\\ C=\left[\begin{array}{lll} 1 & 2 & 4 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{array}\right], \quad D=\left[\begin{array}{lll} 1 & 2 & 4 \\ 0 & 2 & 2 \\ 0 & 0 & 1 \end{array}\right] \text {. } \end{array}\)
Questions & Answers
QUESTION:
Decide (as efficiently as possible) which of the following matrices are diagonalizable. Give your reasoning.
\(\begin{array}{l} A=\left[\begin{array}{lll} 5 & 0 & 2 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{array}\right], \quad B=\left[\begin{array}{lll} 5 & 0 & 2 \\ 0 & 5 & 0 \\ 2 & 0 & 5 \end{array}\right]\\ C=\left[\begin{array}{lll} 1 & 2 & 4 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{array}\right], \quad D=\left[\begin{array}{lll} 1 & 2 & 4 \\ 0 & 2 & 2 \\ 0 & 0 & 1 \end{array}\right] \text {. } \end{array}\)
ANSWER:Step 1 of 4
By the use of Spectral theorem, Let 
1.The eigenvalues of
2.There is an orthonormal basis 
That is, there is an orthogonal matrix 
(a)
Matrix 
