Let 𝐴 = [ 𝑎 𝑏 𝑐 𝑑 ] , where 𝑎 ,   𝑏 ,   𝑐 , and 𝑑 are real numbers. If [ 1 1 ] is an eigenvector of 𝐴 corresponding to the eigenvalue 𝜆 = 4 , find the value of 𝑎 + 𝑏 + 𝑐 + 𝑑 .单项选择题

A

2

B

4

C

8

D

Cannot be determined with the given information.

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已知如下矩阵方程，回答下述问题。 Given the matrix equation below, answer the following questions. 1.哪个是方程中的特征向量？Which is the eigen vector in the equation? 选择 [選擇] 左侧的 2x2 矩阵。The 2x2 matrix on the left. 值为 (1, 1) 的向量 The vector with value (1, 1) 值为 (2, 2) 的向量 The vector with value (2, 2) 值为 (5, 5) 的向量 The vector with value (5, 5) 2.特征值是多少？What is the eigen value? 选择 [選擇] 1 2 3 4 5

特征向量的特征值 𝜆 是指 The eigenvalue  𝜆 of an eigen vector is

Question text 4Marks If [math: [31a]]\left[\matrix{ 3 \cr 1 \cr a } \right] is an eigenvector of [math: A=[3−11−130151],] A = \left[\matrix{ 3 & -1 & 1 \cr -1 & 3 & 0 \cr 1 & 5 & 1 } \right], then [math: a=] Answer 1[input], and the corresponding eigenvalue is [math: λ=]\lambda= Answer 2[input].Notes Report question issue Question 4 Notes

Question textLet [math: A=[210−10−12−14]]A={\left[\begin{array}{ccc} 2 & 1 & 0 \\ -1 & 0 & -1 \\ 2 & -1 & 4 \end{array}\right]}. Find an eigenvector of [math: A] and its corresponding eigenvalue. Note: You don't have to find all eigenvalues and eigenvectors, just a single one will suffice. [table] | | | | | | [/table] Your last answer was interpreted as follows: [math: [1−10]] \left[\begin{array}{c} 1 \\ -1 \\ 0 \end{array}\right] is an eigenvector with eigenvalue [input] Your last answer was interpreted as follows: [math: 1] .

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