95. $\{(y+2w,y,-2y-3w,w)\}$

97.

1. $B=\left[\begin{array}{rrrr}1& {\displaystyle \frac{3}{2}}& 0& -1\\ 0& 1& 0& {\displaystyle \frac{1}{2}}\\ 0& 0& 1& {\displaystyle \frac{1}{2}}\\ 0& 0& 0& 1\end{array}\right],C=\left[\begin{array}{rrrr}1& 2& -3& 1\\ 0& 1& 0& -{\displaystyle \frac{1}{2}}\\ 0& 0& 1& {\displaystyle \frac{1}{2}}\\ 0& 0& 0& 1\end{array}\right]$

2. The reduced row-echelon form of the matrices B and C is $\left[\begin{array}{llll}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]$

99.

1. $\left\{\left({\displaystyle \frac{dm-nb}{ad-bc}},{\displaystyle \frac{an-cm}{ad-bc}}\right)\right\}$

2. 1. $cb\ne ad$

   2. $cb=ad$ and ${\displaystyle \frac{m}{b}}\ne {\displaystyle \frac{n}{d}}$

   3. $cb=ad$ and ${\displaystyle \frac{m}{b}}={\displaystyle \frac{n}{d}}$

101. $\{(10,100,1000)\}$

103. Yes

105. Yes

107. $P(n)=-{\displaystyle \frac{1}{2}}n+{\displaystyle \frac{3}{2}}{n}^2$

109. $\left[\begin{array}{l}0\\ 0\end{array}\right],\left[\begin{array}{l}1\\ 0\end{array}\right]$

111. Yes, the inverse of the operation used to transform A to B