Two factories decided to award their employees for three values of (a) adaptable to new techniques, (b) careful and alert in difficult situations and (c) keeping calm in tense situations, at the rate of ₹x, ₹y and ₹z per persons respectively. The first factory decided to honour respectively 2, 4 and 3 employees with total prize money of ₹29000. The second factory decided to honour respectively 5, 2 and 3 employees with the prize money of ₹30500. If the three prizes per person together cost ₹9500, then

i. represent the above situation by a matrix equation and form linear equations using matrix multiplication.
ii. Solve these equations using matrices.
iii. Which values are reflected in the questions?

Matching exercise

    
Match the items on the right to the items on the left.
Step 1
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Step 3
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Step 5
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Step 8
Let the numbers are x, y,z be the prize amount per person for adaptability, carefulness and calmness respectively.As per the given data we get,
2x + 4y + 3z = 29000
5x + 2y + 3z = 30500
X + y + z = 9500
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|A| = 2(2 – 3) – 4(5 – 3) + 3(5 – 2)= – 1
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