Mathematics: 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

dess ejwjStep-by-step explanation:...

Find the characteristic polynomial of a. use x - id4338912, alinegonzalez0027

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ceibrione1

13.01.2022

The required characteristic polynomial of the given matrix A is x^3+6x+11x+6=0.

Step-by-step explanation: We are given to find the characteristic polynomial of the following 3 × 3 matrix A with unknown variable x :

$A=\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right].$

We know that

for any square matrix M, the characteristic polynomial is given by

|M-xI|=0, where I is an identity matrix of same order as M.

Therefore, the characteristic polynomial of matrix A is

$|A-xI|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right]-x\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\right|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}-x&0&1\\4&-3-x&4\\-2&0&-3-x\end{array}\right] \right|=0\\\\\\\Rightarrow -x(3+x)^2+1(0-6-2x)=0\\\\\Rightarrow (x+3)(-3x-x^2-2)=0\\\\\Rightarrow (x+3)(x^2+3x+2)=0\\\\\Rightarrow x^3+6x+11x+6=0.$

Thus, the required characteristic polynomial of the given matrix A is x^3+6x+11x+6=0.

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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

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