The matrix A is 3 times 5 and 1 2 0 1 1 3 1 1 1 11 1 1 1 1is

The matrix A is 3 times 5 and {(-1 2 0 1 1 },{3 -1 1 -1 1),(1 1 1 1 1)}is a basis for Nul A. Give the rank of A the matrix A is 3 times 5 and {-1 2 0 1 1),(3 -1 1 -1 1),(1 1 1 1 1)} is a basis for Nul A. Give the nullity of A.

Solution

The rank–nullity theorem states that the rank and the nullity of a matrix add up to the number of columns of the matrix.

The number of vectors in the null space of A is the nullity of A. Here, since there are 3 vectors in the basis for Nul A, the nullity of A is 3.

Since A is a 3X5 matrix, as per the rank-nullity theorem, the rank of A + Nullity of A = the number of columns in A i.e rank A + 3 = 5. Therefore rank A = 5 -3 = 2.