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Lisa [10]
3 years ago
13

Which of the following is the solution to the following system of inequalities? x + 2y 2​

Mathematics
1 answer:
tatyana61 [14]3 years ago
7 0

Answer:

2 would be your answer

Step-by-step explanation:

thans

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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
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Answer:  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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