- #1
pyroknife
- 613
- 3
Suppose that T1: V → V and T2: V → V are
linear operators and {v1, . . . , vn} is a basis for V .
If T1(vi) = T2(vi ), for each i = 1, 2, . . . , n, show
that T1(v) = T2(v) for all v in V .
I don't understand this question.
They said If T1(vi) = T2(vi ), for each i = 1, 2, . . . , n
wouldn't that mean T1(v)=T2(v) already? I don't get what I have to prove here.
Isn't this just saying
T1(v1)=T2(v1)
T1(v2)=T2(v2)
.
.
.
T1(vn)=T2(vn)?
linear operators and {v1, . . . , vn} is a basis for V .
If T1(vi) = T2(vi ), for each i = 1, 2, . . . , n, show
that T1(v) = T2(v) for all v in V .
I don't understand this question.
They said If T1(vi) = T2(vi ), for each i = 1, 2, . . . , n
wouldn't that mean T1(v)=T2(v) already? I don't get what I have to prove here.
Isn't this just saying
T1(v1)=T2(v1)
T1(v2)=T2(v2)
.
.
.
T1(vn)=T2(vn)?