Two schools A and B decided to award prizes to their students for three values, team spirit, truthfulness and tolerance at the rate of `R sdotx ,R sdoty` and `R sdotz` per student respectively. School `A` , decided to award a total of Rs. 1,100 for the three values to 3, 1 and 2 students respectively while school B decided to award Rs. 1,400 for the three values to 1, 2 and 3 students respectively. If one prize for all the three values together amount to Rs. 600 then (i) Represent the above situation by a matrix equation after forming linear equations. (ii) Is it possible to solve the system of equations so obtained using matrices ? (iii) Which value you prefer to be rewarded most and why ?

Explanation

`3x+10y+2xz=1100`

`x+2xy+3xz=1400`

`x+y+z=600`

`[[3,1,2],[1,2,3],[1,1,1]][[x],[y],[z]]=[[1100],[1400],[600]]`

`|A|=|[1,2],[2,3]|-1|[3,2],[1,3]|+|[3,1],[1,2]|`

`=(3-4)-(9-2)+(6-1)`

`=-1-7+5=-3!=0`.