# In matrix algebra, what is the value of a-b if the eigenvector of $\begin{pmatrix}1&1&1 \\ 1&1&1 \\ 1&1&1 \end{pmatrix}$ corresponding to eigenvalue three is $\begin{pmatrix}a \\ b \\ a \end{pmatrix}$?

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In matrix algebra, what is the value of a-b if the eigenvector of $\begin{pmatrix}1&1&1 \\ 1&1&1 \\ 1&1&1 \end{pmatrix}$  corresponding to eigenvalue three is $\begin{pmatrix}a \\ b \\ a \end{pmatrix}$?

(a) 0

(b) 1

(c) 2

(d) 3

I have been asked this question in unit test.

The doubt is from Eigen Value and Time Dependent Problems in section Single Variable Problems of Finite Element Method

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The best explanation: If X is an eigenvector corresponding to an eigenvalue L of a matrix K, then KX=LX. The eigenvector of $\begin{pmatrix}1&1&1 \\ 1&1&1 \\ 1&1&1 \end{pmatrix}$ corresponding to eigenvalue three is $\begin{pmatrix}1 \\ 1 \\ 1 \end{pmatrix}$. Equating the corresponding elements of $\begin{pmatrix}a \\ b \\ a \end{pmatrix}$ and $\begin{pmatrix}1 \\ 1 \\ 1 \end{pmatrix}$

a=b=1

a-b=0.

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