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The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping or co-operating others and some (say z) for supervising the workers to keep the colony neat and clean. The sum of all the awardees are 12. Three times the sum of awardees for co-operation and supervision added to two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others. Using matrix method, find the number of awardees of each category.

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x + y + z = 12,

2x + 3y + 3z = 33 and x - 2y + z = 0 

x = 3, y = 4 and z = 5

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