Question

Rank of linea transformation Tis
A Dimension of range space of T
B. Dimension of Null space of T
C. Both of them
D None of them

Answer 1

Linear transformations.

The rank of T is the dimension of the image of T, rank(T)=dim(Im(T)). The nullity of T is the dimension of the kernel of T, nullity(T)=dim(ker(T)). The Rank-Nullity Theorem in its version for linear transformations states that rank(T)+nullity(T)=dim(V).

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