Prove Corollary 3.6.4.
Reference: Corollary 3.6.4:
An n × n matrix A is nonsingular if and only if the column vectors of A form a basis for Rn.
In general, the rank and the dimension of the null space always add up to the number of columns of the matrix. The dimension of the null space of a matrix is called the nullity of the matrix.
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