The rank of a 4×34×3 matrix is 1, what is the dimension of its null space?

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. In this case, the rank of the 4x3 matrix is given as 1.

The dimension of the null space of a matrix, also known as the nullity, is the number of free variables in the system of equations represented by the matrix.

The Rank-Nullity Theorem states that the sum of the rank and the nullity of a matrix is equal to the number of columns in the matrix.

So, in this case, the nullity (dimension of the null space) would be calculated as follows:

Nullity = Number of columns - Rank Nullity = 3 - 1 Nullity = 2

So, the dimension of the null space of the given 4x3 matrix is 2.