Question

7. Let F : V → W be a bijective linear map. Show that the inverse of F is also a linear map.

Answer 1

okk ... assume v1 and v2 are elements of V and w1 and w2 are corresponding images in W then f(v1 + kv2) = w1 + kw2. Also note that this would be exclusive as the function is bijective (one one and onto).

this means that f(x) = w1 if and only if x = v1.

Hence invf(w1 + kw2) = v1 + kv2 = invf(w1) + k * invf(w2) ..

similarly prove for multiplication identity

hence proved..

Answer 2

k thanx....