Find all (real) values of k for which A is diagonalizable. (Enter your answers as a comma-separated list.)A = [4 k0 4 ] k = ___.

Answer:We have the matrix [tex]A=\left[\begin{array}{cc}4&k\\0&4\end{array}\right][/tex]Remember, every symmetric matrix with real coefficients is diagonalizable. Note that the coefficients of A are reals. So, if we take [tex]k[/tex] such that A is symmetric, then A is diagonalizable. For A to be symmetric, [tex]k = a_ {12} = a_ {21} = 0[/tex]Then [tex]k = 0[/tex].