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Let find all values of t such that where I is the 3x3 identity matrix

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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

#1
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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