GATE ME 2019 Set 1 — Question 36
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Engineering Mathematics → Linear Algebra → Consistency of Linear Systems
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Question
The set of equationshas infinite solutions, if
Correct answer
(C) 4
Solution
For a system of linear equations to have infinite solutions, the determinant of the coefficient matrix must be zero, and the rank of the augmented matrix must be equal to the rank of , which must be less than the number of variables (3).The coefficient matrix is .
Setting :
.Case 1:
Augmented matrix
Performing row operations:
Here, . Thus, infinite solutions exist for .Case 2:
Augmented matrix
Here, and . Thus, no solution exists for .
Setting :
.Case 1:
Augmented matrix
Performing row operations:
Here, . Thus, infinite solutions exist for .Case 2:
Augmented matrix
Here, and . Thus, no solution exists for .
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