Suppose A is a 9 times 4 matrix a Is it possible for rank of

Suppose A is a 9 times 4 matrix a) Is it possible for rank of A to equal 9? b) If dimension of Column of A is 2, what is the dimension of Nul(A)? c) Is it possible that Dim(Nul(A)) = 0? d) Is S a subspace of R^3.

Solution

a) Given that A is a 9x4 matrix

No of columns < No of rows = 4

Hence dim of Matrix A can be maximum 4 only.

Cannot be equal to 9.

b) If dim of Col A is 2,

Dim of Null (A) = 4-2 = 2

c) If dim of col A is 4, and rank of A =4 then

dim Null A can be 0