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  4. The characteristic roots of the matrix [ 1&0 &0 2&3& 0 4&5&6 ] are

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Q. The characteristic roots of the matrix $\begin{bmatrix} {1}&{0} &{0}\\ {2}&{3}& {0} \\ {4}&{5}&{6}\\ \end{bmatrix} $ are

KCETKCET 2008Determinants

Solution:

Since, given matrix is a triangular matrix, so its characteristic roots are the diagonal elements.
Hence, required roots are $1, 3, 6$.