GATE EE 2014 Set 1 — Question 11
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Engineering Mathematics → Linear Algebra → Systems of Linear Equations
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Question
Given a system of equations:Which of the following is true regarding its solutions
Correct answer
(B) The system will have infinitely many solutions for any given b₁ and b₂
Solution
The given system of equations is:
1)
2) The coefficient matrix is:The rank of matrix is 2 because the two rows are linearly independent. Since the rank of is equal to the number of equations (full row rank), the system is consistent for any values of and .
However, the number of variables () is greater than the rank (). The number of free variables is . Therefore, the system will have infinitely many solutions for any given and .
1)
2) The coefficient matrix is:The rank of matrix is 2 because the two rows are linearly independent. Since the rank of is equal to the number of equations (full row rank), the system is consistent for any values of and .
However, the number of variables () is greater than the rank (). The number of free variables is . Therefore, the system will have infinitely many solutions for any given and .
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