Linear Equations by Rank Method
Chapter 1: Chapter 1 · MATHEMATICS-VOLUME 1 · EN medium
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In section . . , we have already defined consistency of a system of linear equation. In this section, we investigate it by using rank method. We state the following theorem without proof: Theorem . (Rouché - Capelli Theorem) A system of linear equations, written in the matrix form as AX B , is consistent if and only if the rank of the coefficient matrix is equal to the rank of the augmented matrix; that is, ρ ρ ( ) ([ ]).
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 46
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In section . . , we have already defined consistency of a system of linear equation. In this section, we investigate it by using rank method.
We state the following theorem without proof: Theorem . (Rouché - Capelli Theorem) A system of linear equations, written in the matrix form as AX B , is consistent if and only if the rank of the coefficient matrix is equal to the rank of the augmented matrix; that is, ρ ρ ( ) ([ ]).
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