A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of each kind of officeA.B.C.D.

A finance company has offices located in ewery division, every didtric

1.	A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of each kind of officeA.B.C.D.
Answer» Correct Answer - Total basic monthly salary bill of each division of district and taluka offices an Rs 1675, Rs 675 and Rs 625, respectively. Lets us use the symbols Div, Dis, Tal for division, district, taluka respectively and O, H, C, Cl , T and P for office superintendent, Head clerk, Cashier, Clerk, Typist and Peon respectively. Then the number of offices can be arranged as elements of a row matrix A and the composition of staffin various offices can be areanged in a `3xx6` matrix B (say). `{:(Div, Dis, Tal):}` `therefore A = [[5,30,200]]` and `B=[[1,1,1,2+1,1,1+1],[0,1,1,1+1,0,1+1],[0,1,1,1,0,1]]` or `B= [[1,1,1,3,1,2],[0,1,1,2,0,2],[0,1,1,1,0,1]]` The basic monthly salarise of various types of employees of these offies correspond to the elements of the column matrix C. `thereforeC={:[O],[H],[C],[Cl],[T],[P]:}[[500],[200],[175],[150],[150],[100]]` The total basic monthly salary bill of each kind of office = BC `{:[(O,H,C,Cl,T,P),(1,1,1,3,1,2),(0,1,1,2,0,2),(0,1,1,1,0,1)]:}xx[[500],[200],[175],[150],[150],[100]]{:[O],[H],[C],[Cl],[T],[P]:}` `{:[(500+ 200 + 175+ 3xx 150 + 1xx 150 + 2 xx100),(0+1xx200+1xx175+2xx150+0+2xx100),(0+1xx200+1xx175+1xx150+0+1xx100)]:}` `=[[1675],[875],[625]]` i.e. The total basic monthly salary bill of each divisional, distriict and taluka offices are `Rs 1675, Rs 875 and Rs 625, respectively.

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