107台大資工
(10%) Your answer will be considered correct only if all the true statements are selected. Let A be an nxn matrix. (a) If x1 and x2are the cigenvectors of A, then x1 + x2 is also an eigenvector of A.
(b) If AT = -A, then A is singular.
(c) If A2 = A. (A+1)n = 1 + (2n+1)A.
(d) If A = AT, then A is diagonalizable.
(e) If A =
and B and D are invertible,then
.
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