Mathematics, 26.12.2019 18:31 4waymari
Find the characteristic polynomial of a. use x for the variable in your polynomial. you do not need to factor your polynomial. a = [0 0 1] [ 4 -3 4] [-2 0 -3] 1. haracteristic polynomial of a is
Answers: 1
![A=\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right].](/tpl/images/0433/8861/81772.png)
where I is an identity matrix of same order as M.![|A-xI|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right]-x\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\right|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}-x&0&1\\4&-3-x&4\\-2&0&-3-x\end{array}\right] \right|=0\\\\\\\Rightarrow -x(3+x)^2+1(0-6-2x)=0\\\\\Rightarrow (x+3)(-3x-x^2-2)=0\\\\\Rightarrow (x+3)(x^2+3x+2)=0\\\\\Rightarrow x^3+6x+11x+6=0.](/tpl/images/0433/8861/728f1.png)
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Find the characteristic polynomial of a. use x for the variable in your polynomial. you do not need...
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