110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:線性代數(C)#100943

(a) Find the eigenvalues of A.(5%)

(b) Find a bases for each eigenspace. (5%)

(c) Find an orthogonal matrix Q and diagonal matrix such that Q^TAQ = A. (10%)

( a) One solution.(7%)

(b) No solution. (7%)

(c) Infinitely many solutions. (6%)

(a) det(A).(4%)

(b)(4%)

(c)det(A^TA). (4%)

(d) det(A^T - A).(8%)

5. Let V be a 2-dimensional subspace of and ν₁●ν₂ = 2. Let u = v₁ - 2ν₂ . Find ||ull.(10%)

6. Is L a linear transformation? Why or why not? (10%)

7. Let c be a constant For what values of C is the matrix in the span of S?(10%)