(Solved): Determine \( a \) and \( b \) such that \( A \) is idempotent. (Select all that apply.) \[ \begin{ ...

Determine \( a \) and \( b \) such that \( A \) is idempotent. (Select all that apply.) \[ \begin{array}{l} A=\left[\begin{array}{ll} 1 & a \\ 0 & b \end{array}\right] \\ b=\text { any real number, } a=1 \\ b=0, a=\text { any real number } \\ b=1, a=1 \\ b=1, a=0 \\ b=-1, a=1 \end{array} \] Determine whether the matrix is stochastic. \[ \left[\begin{array}{rr} \frac{5}{7} & -\frac{5}{7} \\ \frac{2}{7} & \frac{12}{7} \end{array}\right] \] In a population of 400,000 people, 160,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune (cannot become infected again). Of the people who are infected, \( 3 \% \) will die each year and the others will recover. Of the people who have never been infected, \( 20 \% \) will become infected each year. How many people will be infected in 4 years? (Round your answer to the nearest whole number.) people Use \( A^{-1} \) to decode the cryptogram. \[ A=\left[\begin{array}{rrr} 1 & 2 & 2 \\ 3 & 7 & 9 \\ -4 & -2 & 11 \end{array}\right] \]