Chapter 7 - Eigenvalues and Eigenvectors - 7.3 Symmetric Matrices and Orthogonal Diagonalization - 7.3 Exercises - Page 371: 39

not orthogonally diagonalizable.

A matrix is symmetric if it is equal to its transpose. Also, a matrix is orthogonally diagonalizable if and only if it is symmetric. Here the transpose of the matrix is $\begin{bmatrix} 4& 0 \\ 5& 1\\ \end{bmatrix} $ which is not the same as the original matrix; thus it is not symmetric and it is not orthogonally diagonalizable.