Without using the concept of the inverse of a matrix, find the matrix such that

Given: =


Multiplying we get,



From above we can see that,


5 x – 7 z = – 16 …(1)


–2x + 3 z = 7 ….(2)


5 y – 7 u = – 6 …..(3)


–2y + 3 u = 2 ……(4)


Now we have to solve these equations to find values of x, y, z and u


Multiplying eq (1) by 2 and eq (2) by 5 and adding the equations we get,


10 x – 14 z + 10 x + 15 z = –32 + 35


Z = 3


Putting this value in eq(1) we get,


5 x – 21 = – 16


5 x = 5


X = 1


Now, multiplying eq(3) by 2 and eq(4) by 5 and adding we get,


10 y – 14 u + 10 y + 15 u = –12 + 10


u = –2


Putting value of u in equation (3) we get,


5 y + 14 = = – 6


5 y = – 20


Y = –4


Therefore now we have,



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