Suppose that A is a 4 times 7 matrix that has an echelon for

Suppose that A is a 4 times 7 matrix that has an echelon form with two zero rows. Find the dimension of the row space of A, the dimension of the column space of A, and the dimension of the null space of A. The dimension of the row space of A is . The dimension of the column space of A is . The dimension of the null space of A is .

Solution

Given that A is matrix of order 4x7 with two zero rows in echlon form. So

Rank of A = number of non-zero rows in echlon form of A = 2

Therefore

dimension of row space of A = rank of A = 2

dimension of column space of A = rank of A = 2

Since, we know that

rank A + nullity A = number of columns of A

2 + nullity A = 7

nullity A = 5

Hence,

dimension of null space of A = nullity A = 5