Question
Download Solution PDFA set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
b must be linearly dependent on the columns of A
Consider A3x3 then [A : b]3x4, i.e., Augmented matrix have 4 vectors.
But by property of rank, we have
Which is definitely less than 4
So [A : b] has L.D. set of vectors so we can conclude that matrix b must be linearly dependent of column of matrix A.
The correct option is (3).
Last updated on Jun 19, 2025
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