Let $I = I _ { 2 }$ Be the Identity Matrix of Order 2, and Let

question 13

Multiple Choice

Let $I = I _ { 2 }$ be the identity matrix of order 2, and let $f ( x ) = | A - x I |$ . Find the polynomial $f ( x )$ for the given matrix A in order to find the zeros of $f ( x )$ .
(In the study of matrices, $f ( x )$ is the characteristic polynomial of A, and the zeros of $f ( x )$ are the characteristic values (eigenvalues) of A.) $$A = \left[ \begin{array} { r r } 37 & - 90 \\12 & - 29\end{array} \right]$$

• A) \(x = 7 , x = 1\)
• B) \(x = - 7 , x = 1\)
• C) \(x = 4 , x = 5\)
• D) \(x = - 10 , x = 6\)
• E) \(x = 7 , x = 4\)

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