True or False Justify your answer Any matrix listed is not a

True or False. Justify your answer. (Any matrix listed is not assumed to be square or invertible unless stated.)

Solution

If A is 4 x 3 matrix , maximum Rank of A = 3

So, A can have maximum 3 pivots i.e. Col(A) = Rank(A) =3

So, Col(A) is a bais of 3 elements, max dimension of Col(A) = 3

Hence it is a subspace of R^4

True