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,