Final answer:
To find the basis of the null space of a matrix, we can row reduce the matrix or perform singular value decomposition (SVD) to identify the pivot variables and use them to form the basis. Each column in the basis can be expressed as a linear combination of the pivot variables.
Step-by-step explanation:
The null space of a matrix consists of all the vectors that when multiplied by the matrix result in the zero vector. To find the basis of the null space, we need to find the vectors that satisfy this property.
To do this, we can row reduce the matrix using Gaussian elimination or perform the singular value decomposition (SVD). We then look for the columns in the reduced or decomposed form that correspond to the pivot variables.
These columns form the basis of the null space. Each column in the basis can be expressed as a linear combination of the pivot variables.