Europe has the lowest population growth rate among continents. This is largely due to low birth rates, aging populations, and, in some regions, migration patterns that offset natural population increase. Many European countries face demographic challenges such as shrinking workforces and increased healthcare demands. Efforts to address these issues include promoting immigration and encouraging higher birth rates through policy measures
Study the following graph carefully and answer the following questions
Study the following table carefully and answer the questions that follow :
Year | Number of Towns/UAs | Urban Population (in Thousands) | % of Total Population | Decennial Growth (%) |
1931 | 2,072 | 33,456.0 | 11.99 | 19.12 |
1941 | 2,250 | 44,153.3 | 13.86 | 31.97 |
1951 | 2,843 | 62,443.7 | 17.29 | 41.42 |
1961 | 2,365 | 78,936.6 | 17.97 | 26.41 |
1971 | 2,590 | 1,09,114 | 19.91 | 38.23 |
1981 | 3,378 | 1,59,463 | 23.34 | 46.14 |
1991 | 4,689 | 2,17,611 | 25.71 | 36.47 |
2001 | 5,161 | 2,85,355 | 27.78 | 31.13 |
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]