考虑以下 2 × 2 矩阵 A，其中两个元素未知并由 a 和 b 标记。该矩阵的特征值为–1 和7。a 和b 的值是什么?
A = | 1 4 |
| b a | (A) a = 6, b = 4
(B) a = 4, b = 6
(C) a = 3, b = 5
(D) a = 5, b = 3答案： (D)
解释：
The character equation for given matrix is
| 1-λ 4 | = 0
| b a-λ|
(1-λ)*(a-λ) - 4b = 0
Putting λ = -1,
=> (1 - (-1)) * (a - (-1)) - 4b = 0
=> 2a + 2 - 4b = 0
=> 2b - a = 1
Putting λ = 7,
=> (1 - 7) * (a - 7) - 4b = 0
=> -6a + 42 - 4b = 0
=> 2b + 3a = 21
Solving the above two equations, we get
a = 5, b = 3
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