3 and 4 .Determinants and Matrices
easy

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 $\mathrm{Y}$.

Option A
Option B
Option C
Option D

Solution

We have

$BA=$  ${\mkern 1mu} \left[ {\begin{array}{*{20}{c}}
 {40,000}&{50,000}&{250,000} \\ 
  {120,000}&{100,000}&{500,000} 
\end{array}} \right]{\mkern 1mu} $ $\begin{array}{*{20}{c}}
   { \to X} \\ 
  { \to \,Y} 
\end{array}$

$ = \,{\mkern 1mu} \left[ {\begin{array}{*{20}{c}}
  {340,000} \\ 
  {720,000} 
\end{array}} \right]{\mkern 1mu} \begin{array}{*{20}{c}}
  {\, \to \,X} \\ 
  { \to \,Y} 
\end{array}$

So the total amount spent by the group in the two cities is $340,000$ paise and $720,000$ paise, i.e., Rs. $3400$ and Rs. $7200,$ respectively.

Standard 12
Mathematics

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