Question

1) Let T : V —> W be a linear transformation with dim(V) = m and...

1) Let T : V —> W be a linear transformation with dim(V) = m and dim(W) = n. For which of the following conditions is T one-to-one?

  1. (A) m>n

  2. (B) range(T)=Wandm=n

  3. (C) nullity(T) = m

  4. (D) rank(T)=m-1andn>m

2) For which of the linear transformations is nullity (T) = 0 ? Why?

(A)T:R3 —>R8 (B)T:P3 —>P3 (C)T:M23 —>M33 (D)T:R5 —>R2

withrank(T)=2 withrank(T)=3 withrank(T)=6 withrank(T)=1

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