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

To solve the problem step by step, we will break it down into parts as described in the question.

### Step 1: Forming Linear Equations

1. **For School A**:
- Let the amounts awarded for team spirit, truthfulness, and tolerance be Rs. X, Rs. Y, and Rs. Z respectively.
- School A awards Rs. 1100 in total to 3 students for team spirit, 1 student for truthfulness, and 2 students for tolerance.
- The equation for School A can be written as:
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