If $A = \left[ {\begin{array}{*{20}{c}}0&1 \\ 1&0\end{array}} \right],$then ${A^4}$=

In a legislative assembly election, a political group hired a public relations firm to promote its candidate in three ways: telephone, house calls, and letters. The cost per contact (in paise) is given in matrix $A$ as

$A = \left[ {\begin{array}{*{20}{c}}
  {\mathrm {Cost\,\,per\,\,contact}} \\ 
  {40} \\ 
  {100} \\ 
  {50} 
\end{array}} \right]\begin{array}{*{20}{l}}
  {{\text{ Telephone }}} \\ 
  {{\text{ Housecall }}} \\ 
  {{\text{ Letter }}} 
\end{array}$

The number of contacts of each type made in two cities $\mathrm{X}$ and $\mathrm{Y}$ is given by

$B=$$\,\left[ {\begin{array}{*{20}{c}}
  {\mathrm {Telephone}}&{\mathrm {Housecall}}&{\mathrm {Letter}} \\ 
  {1000}&{500}&{5000} \\ 
  {3000}&{1000}&{10,000} 
\end{array}} \right]\,$ $\begin{array}{*{20}{c}}
  {} \\ 
  { \to X} \\ 
  { \to \,Y} 
\end{array}$.  Find the total amount spent by the group in the two cities $\mathrm{X}$ and $\mathrm{Y}$.

If $\left[ {\begin{array}{*{20}{c}}1&2&3\\3&1&2\\2&3&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ {\begin{array}{*{20}{c}}4&{ – 2}\\0&{ – 6}\\{ – 1}&2\end{array}} \right]\,\left[ \begin{array}{l}2\\1\end{array} \right]$, then $(x,y,z)$=

If $p, q, r$ are $3$ real numbers satisfying the matrix equation, $[p\,q\,r]\,\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]$ then $2p + q – r$ equals

If $\left[ {\begin{array}{*{20}{c}}{x + y}&{2x + z}\\{x – y}&{2z + w}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}4&7\\0&{10}\end{array}} \right]$, then values of $x, y, z, w$ are