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Loser66
 one year ago
Let A be a 2x2 matrix for which there is a constant k such that the sum of the entries in each row and each column is k. Which of the following must be an eigenvector of A?
I) (1,0)
II) (0,1)
III)(1,1)
A) I only
B) II only
C) III only
D) I, II
E)I,II,III
Please, help.
Loser66
 one year ago
Let A be a 2x2 matrix for which there is a constant k such that the sum of the entries in each row and each column is k. Which of the following must be an eigenvector of A? I) (1,0) II) (0,1) III)(1,1) A) I only B) II only C) III only D) I, II E)I,II,III Please, help.

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.1As usual, I would like to know there is any shortcut to find the answer or I have to go step by step to find eigenvectors of A?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1It is not hard to see that the matrix will be of form \[\begin{bmatrix} a&b\\b&a\end{bmatrix}\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Next i would multiply each of the given eigen vectors and see if any makes sense

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Hence, only one way!!! right? do steps, right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\begin{bmatrix} a&b\\b&a\end{bmatrix} \begin{bmatrix}1\\0\end{bmatrix}~~ \stackrel{?}{=}~~ \lambda \begin{bmatrix} 1\\0\end{bmatrix}\]

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1if a = lambda and b = 0 but if it is, then the \(A  I\lambda\) is a zero matrix> no more lambda
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