GATE EC 2022 Set 1 — Question 12
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Engineering Mathematics → Linear Algebra → Existence & Uniqueness
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Question
Consider a system of linear equations , whereThis system of equations admits _________.
Correct answer
(C) no solutions for x
Solution
To determine the nature of the solutions for the system , we examine the rank of the coefficient matrix and the augmented matrix .The augmented matrix is:Performing the row operation :From the row-echelon form:
1.The rank of the coefficient matrix , (number of non-zero rows in the part).
2.The rank of the augmented matrix , (number of non-zero rows in the full augmented matrix).
According to the Rouché–Capelli theorem, a system of linear equations is consistent if and only if the rank of the coefficient matrix is equal to the rank of the augmented matrix. Since (), the system is inconsistent and has no solution.Continue learning with Success Tracker
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