10 students were selected from a school on the basis of values for giving awards and were divided into three groups.

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10 students were selected from a school on the basis of values for giving awards and were divided into three groups. The first group comprises hard workers, the second group has honest and law abiding students and the third group contains vigilant and obedient students. Double the number of students of the first group added to the number in the second group gives 13, while the combined strength of first and second group is four times that of the third group. Using matrix method, find the number of students in each group. Apart from the values, hard work, honesty and respect for law, vigilance and obedience, suggest one more value, which in your opinion, the school should consider for awards.

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Let no. of students in Ist, 2nd and 3rd group to x, y, z respectively.

From the statement we have

x + y+ z = 10

2x + y =13

x + y – 4z = 0

The above system of linear equations may be written in matrix form as AX = B where Now, A11 = – 4 – 0 = –4

A12 = – (–8 – 0) = 8

A13 = 2 – 1 = 1

A21 = –(–4 – 1) = 5

A22 = –4 – 1 = –5

A23 = –(1 – 1) = 0

A31 = 0 – 1 = –1

A32 = –(0 – 2) = 2

A33 = 1 – 2 = –1 