所屬科目：台大◆電機◆離散數學(B)
1. Let
where x ∈ R. Determine the rank of A according to the value of x.
(i)
(ii)
(iii)
(i) all eigenvalues of A;
(ii) all eigenvectors of A;
(iii) a diagonal matrix D and an invertible matrix C such that A = .
(i) the row space of A;
(ii) the column space of A;
(iii) the null space of A.
6. Employ the technique of Lagrange multipliers to find the maximum and minimum of 'f(x, y) = xy x subject to the constraint x² + y² = 1.
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