GATE CS 2014 Set 1 — Question 14
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Engineering Mathematics → Linear Algebra → System of Linear Equations
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Question
Consider the following system of equations:The number of solutions for this system is __________________
Correct answer
1 to 1
Solution
We have the system of equations:
1)
2)
3)
4) From (1), .
Substitute into (3):
.Substitute into (2):
.Now find :
.Now find :
.We have a unique candidate solution .
We must verify if this satisfies the fourth equation (4):
.The solution satisfies all equations. Since the system is linear and we found a unique solution by substitution, there is exactly 1 solution.
1)
2)
3)
4) From (1), .
Substitute into (3):
.Substitute into (2):
.Now find :
.Now find :
.We have a unique candidate solution .
We must verify if this satisfies the fourth equation (4):
.The solution satisfies all equations. Since the system is linear and we found a unique solution by substitution, there is exactly 1 solution.
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