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The sum of the eigenvalues of the matrix (5412)\begin{pmatrix} 5 & 4 \\1 & 2\end{pmatrix}(51​42​) is​
Question

The sum of the eigenvalues of the matrix (5412)\begin{pmatrix} 5 & 4 \\1 & 2\end{pmatrix} is​

A.

2

B.

7

C.

3

D.

1

Correct option is B

Given matrix: A=(5412)Sum of eigenvalues of a matrix=Trace of the matrixTrace(A)=5+2=7Sum of eigenvalues=7\text{Given matrix: } A = \begin{pmatrix} 5 & 4 \\ 1 & 2 \end{pmatrix} \\\text{Sum of eigenvalues of a matrix} = \text{Trace of the matrix} \\\text{Trace}(A) = 5 + 2 = 7 \\\therefore \text{Sum of eigenvalues} = 7


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