Multiple choice

The minimum and the maximum eigen values of the matrix $\begin{bmatrix} \ 1 & 1 & 3 \\ \ 1 & 5 & 1 \\ \ 3 & 1 & 1 \\ \end{bmatrix}$ are - 2 and 6 respectively. What is the other eigen value?

  1. 5

  2. 3

  3. 1
    • 1
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B Correct answer
Explanation

For a matrix, the sum of the eigenvalues equals the trace of the matrix. The trace is 1 + 5 + 1 = 7. Given eigenvalues are -2 and 6, let the third be x. Then -2 + 6 + x = 7, which gives x = 3.

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