In a survey of 20 richest persons of three cities A, B, C it is found that in city A, - Maths - Matrices

Question

In a survey of 20 richest persons of three cities A, B, C it is
found that in city A, 5 believe in honesty, 10 in hard work & 5
in unfair means, ​while in city B, 5 believe in honesty, 8 in
hard work & 7 in unfair means, and in city C, 6 believe in
honesty, 8 in hard work & 6 in unfair means If the per day
income of these richest persons of cities A, B, C are Rs 3 lakh, Rs
5 lakh, Rs 4 lakh respectively, then find the per day income of
each type of person by matrix method

Shivam Mishra · Accepted Answer

Dear Student, Please find below the solution to the asked query: Let per day income of honest person x units, that of hard working person be y units and that of peoplewho believe in unfair means be z units For city A5x+10y+5z=3 ;i 3 means 3 lakhsFor city B5x+8y+7z=5 ;iiFor city C6x+8y+6z=4⇒3x+4y+3z=2 ;iiiWriting i,ii,iii in matrix form we get:5105587343xyz=352PX=Q⇒X=P-1QSo now we need to find inverse of 5105587343I will find it by elementary row method You can find it by cofactor method

Let per day income of honest person x units, that of hard working person be y units and that of peoplewho believe in unfair means be z units For city A5x+10y+5z=3 ;i 3 means 3 lakhsFor city B5x+8y+7z=5 ;iiFor city C6x+8y+6z=4⇒3x+4y+3z=2 ;iiiWriting i,ii,iii in matrix form we get:5105587343xyz=352PX=Q⇒X=P-1QSo now we need to find inverse of 5105587343I will find it by elementary row method You can find it by cofactor method So we have:xyz=-15-12323100-12-1512-12352=-35-52+3910+0-1-35+52-1=-0 1-0 10 9⇒x=-0 1 and y=-0 1 and z==0 9But x and y cannot be negative Hence given data is incorrect But you should follow the same approach in these type of questions Hope this information will clear your doubts about this topic If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible Regards