Nullity of a Matrix Last Updated : 12 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Prerequisite – Mathematics | System of Linear Equations Let A be a matrix. Since, number of non-zero rows in the row reduced form of a matrix A is called the rank of A, denoted as rank(A) and Nullity is the complement to the rank of a matrix .Please go through the Prerequisite first and read the rank topic, then come to this topic. Therefore, Nullity of a matrix is calculated from rank of the matrix using the following steps:Let A[m*n] matrix, then: Calculate rank (r) of the Matrix. Use The Rank Plus Nullity Theorem, it says Nullity + rank = number of columns (n) Therefore, you will be able to calculate nullity as Nullity = no. of columns(n) - rank(r) Consider the examples: Example-1: Input: mat[][] = {{10, 20, 10}, {20, 40, 20}, {30, 50, 0}} Output: Rank is 2 and hence Nullity is 1 Explanation: Ist and IInd rows are linearly dependent. But Ist and 3rd or IInd and IIIrd are independent, so Rank is 2 and hence Nullity is (3-2) = 1. Example-2: Input: mat[][] = {{1, 2, 1}, {2, 3, 1}, {1, 1, 2}} Output: Rank is 3 and hence Nullity is 0 Explanation: Ist and IInd and IIIrd rows are linearly dependent, so Rank is 3 and hence Nullity is (3-3) = 0. Comment More infoAdvertise with us B bhanu5686 Follow Improve Article Tags : Engineering Mathematics Similar Reads Engineering Mathematics Tutorials Engineering mathematics is a vital component of the engineering discipline, offering the analytical tools and techniques necessary for solving complex problems across various fields. Whether you're designing a bridge, optimizing a manufacturing process, or developing algorithms for computer systems, 3 min read Linear AlgebraMatricesMatrices are key concepts in mathematics, widely used in solving equations and problems in fields like physics and computer science. 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