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] .多项填空题

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Question textSuppose a [math: 4×4] matrix has four eigenvalues [math: −1], [math: 2], [math: 1+i] and [math: 1−i]. What is the maximum number of linearly independent eigenvectors corresponding to the eigenvalue [math: 2]?Answer: Answer 1 Question 2[input]
Question text The characteristic polynomial of the matrix [math: [1−63−61−3015−5]] has the form [math: −λ3+α2λ2+α3λ+α4]. Find [math: α2,α3] and [math: α4].[math: α2=]Answer 1 Question 3[input], [math: α3=]Answer 2 Question 3[input], [math: α4=]Answer 3 Question 3[input].The eigenvalue [math: λ=−5] has an eigenvector [math: [−1mn]], find [math: m] and [math: n]. Then [math: m=]Answer 4 Question 3[input], [math: n=]Answer 5 Question 3[input].
Question textSuppose a [math: 4×4] matrix has four eigenvalues [math: −1], [math: 2], [math: 1+i] and [math: 1−i]. What is the maximum number of linearly independent eigenvectors corresponding to the eigenvalue [math: 2]?Answer: Answer 1 Question 2[input]
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
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