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Let \({A} = \begin{pmatrix} 0 & 5 & 7 \\ -2 & 7 & 7 \\ -1 & 1 & 4 \end{pmatrix}.\) find all values of t such that \(\det (t {I} - {A}) = 0\) where I is the 3x3 identity matrix

 May 14, 2022
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After simplifying the determinant in \(\det(tI - A) = 0\), you will get \(-40 + 38 t - 11 t^2 + t^3 = 0\). Then you can solve the cubic equation to find the values of t.

 

Hint: \(-40 + 38 t - 11 t^2 + t^3 = (t - 2)(t - 4)(t - 5)\).

 May 14, 2022

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