Mark the following either true or false. Justification is required. (a) The dimensions of Col A and Nul A add up to the number of rows of A. (b) If B is a basis of subspace H, then each vector in H can be written in one and only one way as a linear combination of the vectors in B. (c) The dimension of Nul A is the number of free variables in the equa- tion Az = 0.

To answer the questions we can use following formula

(a) For a matrix A with order m × n, 

Rank (A) + Nullity (A) = Number of columns in A

(b) Elements of a basis vectors are linearly independent.

(c) Using rank nullity theorem,

number of columns of A - Rank of A = nullity of A