Question

Two cricket teams honored their players for three values, excellent

batting, to the point bowling and unparalleled fielding by giving x, y

and z per player respectively. The first team paid respectively 2, 2

and 1 players for the above values with a total prize money of 11 lakhs,

while the second team paid respectively 1,2 and 2 players for these

values with a total prize money of 9 lakhs. If the total award money

for one person each for these values amount to 6 lakhs, then express

the above situation as a matrix equation and find award money per

person for each value.

For which of the above mentioned values, would you like more and

why

Answer 1

I would like, to the point bowling ,as the whole match depends mainly on the bowling .
I hope it helps you.....

Answer 2

Given:

Two cricket teams honored their players for three values, excellent   batting, to the point bowling and unparalleled fielding by giving x, y  and z per player respectively.

The first team paid respectively 2, 2  and 1 players for the above values with a total prize money of 11 lakhs.

The second team paid respectively 1,2 and 2 players for these  values with a total prize money of 9 lakhs.

The total award money  for one person each for these values amount to 6 lakhs.

To Find:

Award money per  person for each value.

Solution:

Given x , y and z are the prize money allocated for each quality.

• x = excellent batting

• y = point bowling

• z = unparalleled fielding

Now,

Condition 1 :

• 2x + 2y + z = 11 Lakhs
• x + 2y + 2z = 9 Lakhs
• x + y  + z = 6 Lakhs

In Matrix form :

• $\left[\begin{array}{ccc}2&2&1\\1&2&2\\1&1&1\end{array}\right]$$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]$ = $\left[\begin{array}{ccc}11\\9\\6\end{array}\right]$
• Applying some transformations:
• 2 x Row3  - Row1 --> Row3
• Then applying,
• 2xRow2 - Row1 --> Row2
• $\left[\begin{array}{ccc}2&2&1\\0&2&3\\0&0&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]$ = $\left[\begin{array}{ccc}11\\7\\1\end{array}\right]$

Now,

• Row2 -3xRow3 -> Row2

• $\left[\begin{array}{ccc}2&2&1\\0&2&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]$ = $\left[\begin{array}{ccc}11\\4\\1\end{array}\right]$  

Therefore,

• z = 1 Lakhs
• y = 4/2 Lakhs = 2 Lakhs
• 2x + 4 + 1 = 11
• x = 3 Lakhs

Award Money per person for each value is 3 Lakhs for batting, 2 Laksh for bowling and 1 Lakhs for fielding.