Question

(1) Let T: Rn--->Rm be linear tranformations.

Answer 1

Answer:

Check the explanation

Step-by-step explanation:

1.

(a)

n>=m

(b)

n <= m

(c)

n=m

2.

(a)

let T(v1) = T(v2)

=>

T(v1)-T(v2) = 0

=>

T(v1-v2) = 0

=>

v1-v2 = 0 from the hypothesis

=>

v1=v2

=>

T is one-one

thus proved

(b)

lets assume T is onto, we already know that T is one-one, so from above problem (third case where m=n)

we should have 3=4 which is impossible

so T is NOT onto.

3.

we need to find a,b such that

T(a,b) =(a,b)

=>

a= b

=>

points on the line x=y are the required points