試題詳解

10. Let A be an nxn matrix and b be an arbitrary nx1 vector. Select the incorrect arguments.
(A) If determinant det（A）≠ 0, then the system equation Ax=b has exactly one single solution.
(B) If matrix A is diagonalizable, then the system equation Ax=b has exactly one single solution.
(C) Let matrix A can be decomposed into A=QR, where Q is the orthogonal matrix and R is the upper triangular matrix: The system equation Ax=b has exactly one single solution.
(D) Let matrix A have n independent eigenvectors. The matrix A should have n distinct eigenvalues.
(E) The system equation Ax=b can be solved by Cramer's rule either the system is consistent or inconsistent.