For a real symmetric matrix $[\mathbf{A}],$ which of the following statements is true:

(A) The matrix is always diagonalizable and invertible.

(B) The matrix is always invertible but not necessarily diagonalizable.

(C) The matrix is always diagonalizable but not necessarily invertible.

(D) The matrix is always neither diagonalizable nor invertible.

For a real symmetric matrix $[\mathbf{A}],$ which of the following statements is true:

(A) The matrix is always diagonalizable and invertible.

(B) The matrix is always invertible but not necessarily diagonalizable.

(C) The matrix is always diagonalizable but not necessarily invertible.

(D) The matrix is always neither diagonalizable nor invertible.

1 Answer - 5876 Votes

3537

(C) The matrix is always diagonalizable but not necessarily invertible.