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Tems11 [23]
3 years ago
12

For the matrices below. Find all (real) eigenvalues. A= [7 9] [0 9]

Mathematics
1 answer:
Jet001 [13]3 years ago
8 0

Answer:

The answer is "9 and 7".

Step-by-step explanation:

Given:

A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right]

Using formula:

|A-\lambda \cdot I|= 0\\\\

\to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\

\to \lambda=7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lambda=9\\\\

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The rectangle below has an area of x2 + 11x + 28 square meters and a length of 2 + 7 meters.
Troyanec [42]
<h3><u>Question:</u></h3>

The rectangle below has an Área of x^2 + 11x + 28 square meters and a length of x+7 meters. What expression represents the width of the rectangle?

<h3><u>Answer:</u></h3>

The expression representing width of rectangle is (x + 4) meters

<h3><u>Solution:</u></h3>

Given that rectangle has an area x^2 + 11x + 28 square meters and a length of x + 7 meters

To find: width of the rectangle

<em><u>The area of rectangle is given as:</u></em>

\text {Area of rectangle }=\text { length } \times \text { width }

Here area = x^2 + 11x + 28 square meters

length = x + 7 meters

<em><u>Substituting the values in given formula,</u></em>

\begin{array}{l}{\text { width }=\frac{x^{2}+11 x+28}{x+7}} \\\\ {\text { width }=\frac{x^{2}+4 x+7 x+28}{x+7}} \\\\ {\text { width }=\frac{x(x+4)+7(x+4)}{x+7}} \\\\ {\text { width }=\frac{(x+4)(x+7)}{x+7}}\end{array}

Cancelling (x + 7) on numerator and denominator,

\text { width }=(x+4)

Thus expression representing width of rectangle is (x + 4) meters

3 0
3 years ago
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