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

127 votes

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

127 votes

127