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finlep [7]
3 years ago
11

A 50-foot ladder leans against a wall, as shown in the figure below. If the base of the ladder is 30 feet away from the wall, ho

w tall is the wall?
Select one:
A. 3
B. 4
C. 5
D. 40
Mathematics
1 answer:
tamaranim1 [39]3 years ago
4 0
Pythagorean theorem gives u answer d. Ill include work for you in chat
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Answer:  The required characteristic polynomial of the given matrix A is x^3+6x+11x+6=0.

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

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

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|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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