Final answer:
The nullspace of a 2x3 matrix a, which contains the vector (1, 2, 3), is the set of all scalar multiples of this vector. It is a subspace spanned by the vector (1, 2, 3).
Step-by-step explanation:
The nullspace of a matrix, also known as the kernel, is the set of all vectors that when multiplied by the matrix result in the zero vector. If we're given that the vector (1, 2, 3) belongs to the nullspace of a 2x3 matrix a, it means that when this matrix is multiplied by the column vector
[1 2 3]T, the result is the zero vector.
To find the nullspace of the matrix a, we must find all vectors v such that a*v = 0. Given that (1, 2, 3) is in the nullspace of a, any scalar multiple of this vector will also be in the nullspace. The nullspace can be expressed as the set of all vectors x is a scalar.
Therefore, the nullspace of matrix a is a subspace spanned by the single vector (1, 2, 3), and any vector in the nullspace can be written as a scalar multiple of this vector.