3. Considere la matriz \[ A=\left(\begin{array}{rrr}3 & -1 & -1 \\ 1 & 1 & -1 \\ 1 & -1 & 1\end{array}\right) \] cuyo polinomio característico es \( p(\lambda)=(1-\lambda)(\lambda-2)^{2} \). (a) (10 puntos) Determine el espacio propio asociado a \( \lambda=1 \). (b) \( (10 \) puntos) Determine el espacio propio asociado a \( \lambda=2 \). (c) \( (4 \) puntos) iEs \( A \) diagonalizable? En caso que lo sea explicite las matrices \( P \) y \( D \) que verifican \( P^{-1} A P=D \).

Activity 4.3 .1 - Write a Summary "Japanese Internment Camp Locations" By Rebecca K. Sharp "Beginning in May 1942, the War Department transferred the Japanese Americans to 10 War Relocation Authority (WRA) relocation centers: Central Utah (Utah), Colorado River (Arizona), Gila River (Arizona), Granada (Colorado), Heart Mountain (Wyoming), Jerome (Arkansas), Manzanar (California), Minidoka (Idaho), Rohwer (Arkansas), and Tule Lake (California). Under guard and surrounded by barbed-wire fences, the internees lived in cramped barracks sharing communal toilets, showers, and mess halls. Privacy was nonexistent. The relocation centers mirrored small communities with churches, hospitals, libraries, post offices, and schools. The WRA allowed some internees to leave for temporary seasonal agricultural work. Others attended college, served in the military, or obtained outside employment. Some of the internees remained in the WRA relocation centers until they closed in 1946."

Hausaufgabe 23: (Inverse einer Matrix) a) Berechnen Sie die Inverse der Matrix \[ A=\left(\begin{array}{ccc}0 & -3 & -2 \\ 1 & -4 & -2 \\ -3 & 4 & 1\end{array}\right), \] indem Sie die Matrix \( A^{-1} \) in allgemeiner Form ansetzen und ihre unbekannten Matrix- elemente über die Forderung \( A A^{-1}=\mathbf{1}_{3} \) ermitteln. b) Prüfen Sie Ihr Ergebnis aus a), indem Sie das Matrixprodukt \( A A^{-1} \) ausführen. (Die Be- rechnungen der Einträge in der 1. Spalte von \( A A^{-1} \) sind dabei detailliert aufzuschreiben.)

What action does the USDA believe could save the United States \( \$ 200 \) million per year in fuel costs? A) increasing irrigation efficiency (B) increasing food prices (C) decreasing dairy farmers Decreasing population growth

6. How did the pandemic highlight the interconnectedness of global communities? 7. What can you infer about the adaptability of schools and businesses during the pandemic? 8. How did people's understanding of the virus evolve over time, and what factors contributed to this change?

2 is a quadratic residue modulo 5