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Principal and staff of a school decided to award prizes to their students for three values Honesty (x) cleanliness (y), Punctuality (z) in two groups. Group A ( upto class VIII) and group B ( IX - XII). It is decided that Rs. 12000 for three values (x, y, z) for 3, 4, 5 students of Group A and Rs. 11040 for 5, 4, 3 student of group B respectively. If all the three prizes together amount to Rs. 2880, then (i) Represent above situation by a matrix equation and form linear equation using matrices. (ii) Is it possible to solve the system of linear equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why?

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