Q.Two farmers Shantaram and Kantaram cultivate three crops rice, wheat and groundnut. The sale (In Rupees) of these crops by both the farmers for the month of April and May 2008 is given below: April sale (Rs.) — Shantaram: Rice 15000, Wheat 13000, Groundnut 12000; Kantaram: Rice 18000, Wheat 15000, Groundnut 8000. May sale (Rs.) — Shantaram: Rice 18000, Wheat 15000, Groundnut 12000; Kantaram: Rice 21000, Wheat 16500, Groundnut 16000. Find the increase in sale from April to May for every crop of each farmer.

Matrices of the same order can be checked for equality ($A=B$ iff every corresponding entry matches), added ($A+B=[a_{ij}+b_{ij}]$, entry-by-entry, undefined for mismatched orders), subtracted ($A-B=A+(-B)$), and scaled by a number ($kA=[k\,a_{ij}]$, every entry multiplied by $k$). These operations obey familiar-looking laws — addition is commutative ($A+B=B+A$) and associative ($(A+B)+C=A+(B+C)$), the zero matrix is the additive identity, $-A$ is the additive inverse, and scalar multiplication distributes over both matrix sums and scalar sums. The most common use is solving a linear matrix equation for an unknown matrix $X$ (e.g. $3A-4B+5X=C$): treat $X$ exac …