Eigenvalue placement

Algebra Level pending

Let

A = [ 1 5 2 3 ] A = \begin{bmatrix} 1 && 5 \\ -2 && 3 \end{bmatrix}

and let

B = A [ 1 2 ] [ k 1 k 2 ] B = A - \begin{bmatrix} 1 \\ 2 \end{bmatrix} \begin{bmatrix} k_1 && k_2 \end{bmatrix}

Find k 1 k_1 and k 2 k_2 such that the eigenvalues of B B are 2 - 2 and 3 -3 , and enter the value of 72 k 1 + 27 k 2 72 k_1 + 27 k_2


The answer is 193.

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