Let A = R – {3} and B = R – {1}. Consider the function f : A B defined by . Show that f is one-one and onto and hence find f - 1.
Using matrices solve the following system of linear equations:
x - y + 2 z = 7
3 x + 4 y - 5 z = - 5
2 x - y + 3 z = 12
The given system of equation can be written in the form of AX = B, where
Now,
Thus, A is non-singular. Therefore, its inverse exists.
Now, A11 = 7, A12 = - 19, A13 = - 11
A21 = 1, A22 = - 1, A23 = - 1
A31 = - 3, A32 = 11, A33 = 7