Question

Let T be a linear transformation from a vector space V with dimension 11 onto a vector space W with dimension 7. What is the dimension of the nullspace of T?

Answer 1

Answer:

The dimension of the nullspace of T = 4

Explanation:

The rank/dimension theorem is explains that:

Suppose V and W are vector spaces over F, and T:V → W is linear. If V is finite dimensional, then

nullity(T) + rank(T) = dim(V).

rank(T) = dimension of T = dim(T) = dim(W) = 7

nullity(T) = dimension of the nullspace of T = dim(T) = ?

dim(V) = 11

nullity(T) = dim(V) - dim(T) = 11 - 7

nullity(T) = 4.