#4| GATE 2021 Question | Rank and Nullity in Homogeneous | Linear Algebra

GATE 2021 Question | Rank and Nullity in Homogeneous | Linear Algebra #gatepyqs #gatecse #gate
🔥 Welcome to our channel! In this exclusive GATE 2021 solution video, we tackle a challenging linear algebra question from the previous year's exam. We'll help you master the concept of matrix rank and provide a step-by-step approach to find the rank of a 4x5 matrix, P.
🎯 Problem Statement: We're given a matrix P such that every solution of the equation Px = 0 is a scalar multiple of the vector [2 5 4 3 1]^T. Our goal is to determine the rank of matrix P based on this unique condition.
💡 Key Concepts Covered:
Understanding matrix rank and its significance.
Properties of the null space and its connection to scalar multiples.
Solving linear equations involving matrices.
📚 Prerequisites: Basic knowledge of matrices, linear algebra, and vectors will be beneficial, but we'll explain the essential concepts as we progress through the solution.
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