$$ \begin{array}{l} \left(1330-0.3567 \lambda_{i} ight)\left|\begin{array}{cc} 1210-0.3261 \lambda_{i} & -560 \ -560 & 560-0.2956 \lambda_{i} \end{array} ight|-(-560)\left|\begin{array}{cc} -650 & -560 \ 0 & 560-0.2956 \lambda_{i} \end{array} ight|=0 \end{array} $$

Question

$$ \begin{array}{l} \left(1330-0.3567 \lambda_{i}ight)\left|\begin{array}{cc} 1210-0.3261 \lambda_{i} & -560 \ -560 & 560-0.2956 \lambda_{i} \end{array}ight|-(-560)\left|\begin{array}{cc} -650 & -560 \ 0 & 560-0.2956 \lambda_{i} \end{array}ight|=0 \end{array} $$

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$\lambda$$:
  $$\left(1330-0.3567\lambda \right)\times \left|\begin{array}{cc}{1210-0.3261\lambda }&{-560}\{-560}&{560-0.2956\lambda }\end{array}\right|-\left(-560\right)\times \left|\begin{array}{cc}{-650}&{-560}\{0}&{560-0.2956\lambda }\end{array}\right|=0$$
- step1: Simplify:
  $$\left(1330-0.3567\lambda \right)\left(364000-540.292\lambda +0.09639516\lambda ^{2}\right)-203840000+107598.4\lambda =0$$
- step2: Calculate:
  $$280280000-740828.76\lambda +320.9277192\lambda ^{2}-\frac{8596038393}{250000000000}\lambda ^{3}=0$$
- step3: Factor the expression:
  $$\frac{1}{250000000000}\left(280280000\times 250000000000-185207190000000000\lambda +80231929800000\lambda ^{2}-8596038393\lambda ^{3}\right)=0$$
- step4: Divide both sides:
  $$280280000\times 250000000000-185207190000000000\lambda +80231929800000\lambda ^{2}-8596038393\lambda ^{3}=0$$
- step5: Calculate:
  $$\begin{align}&\lambda \approx 5934.443288\&\lambda \approx 468.731421\&\lambda \approx 2930.418992\end{align}$$
- step6: Rewrite:
  $$\lambda_{1}\approx 468.731421,\lambda_{2}\approx 2930.418992,\lambda_{3}\approx 5934.443288$$
La ecuación dada es:

$$
\left(1330-0.3567 \lambda_{i}\right)\left|\begin{array}{cc}
1210-0.3261 \lambda_{i} & -560 \
-560 & 560-0.2956 \lambda_{i}
\end{array}\right|-(-560)\left|\begin{array}{cc}
-650 & -560 \
0 & 560-0.2956 \lambda_{i}
\end{array}\right|=0
$$

Al resolver esta ecuación, encontramos los siguientes valores para $$ \lambda_{i} $$:

1. $$ \lambda_{1} \approx 468.731421 $$
2. $$ \lambda_{2} \approx 2930.418992 $$
3. $$ \lambda_{3} \approx 5934.443288 $$

Estos son los valores aproximados de $$ \lambda_{i} $$ que satisfacen la ecuación.
Los valores de $$ \lambda_{i} $$ que satisfacen la ecuación son aproximadamente 468.73, 2930.42, y 5934.44.

\( \begin{array}{l} \left(1330-0.3567 \lambda_{i}\right)\left|\begin{array}{cc} 1210-0.3261 \lambda_{i} & -560 \\ -560 & 560-0.2956 \lambda_{i} \end{array}\right|-(-560)\left|\begin{array}{cc} -650 & -560 \\ 0 & 560-0.2956 \lambda_{i} \end{array}\right|=0 \end{array} \)

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