A school wants to award its student for the values of honesty,regularity and hard work with a total cash award of RS. 6000.Three times the award money for hardwork added to that given for honesty amounts to RS 11000.The award money given for honesty and hard work together is double the one given for regularity.Represent the above situation algebraically and find the award money for each value,using matrix method.apart from these values ,namely, honesty, regularity and hardwork, suggest one more value which the school must include for awards?

Let the award money given for Honesty, Regularity and Hard work be  respectively.

Since total cash award is Rs 6000. Therefore,

Three times the award money for Hard work added to given for Honesty amounts to Rs 11,000. Therefore,

Award money for Honesty and Hard work together is double the one given for regularity. Therefore,

The above system of equations can be written in matrix form AX=B as,

Where,

 

Now,

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