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Consider matrix 
The number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________
The number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer?
Verified Answer
Consider matrixThe number of distinct real values of k for which the e...
Concept:
We can find the consistency of the given system of equations as follows:
(i) If the rank of matrix A is equal to the rank of an augmented matrix and it is equal to the number of unknowns, then the system is consistent and there is a unique solution.
The rank of A = Rank of augmented matrix = n
(ii) If the rank of matrix A is equal to the rank of an augmented matrix and it is less than the number of unknowns, then the system is consistent and there are an infinite number of solutions.
The rank of A = Rank of augmented matrix < n
Then |A| = 0
(iii) If the rank of matrix A is not equal to the rank of the augmented matrix, then the system is inconsistent, and it has no solution.
The rank of A ≠ Rank of an augmented matrix
Application:
A system to have infinitely many solutions must satisfy:
|A| = 0
K2 (K – 2(K – 1) = 0
K2 (K – 2K + 2) = 0
K2 (-K + 2) = 0
K = 0, 0, 2
Hence, there are 3 eigen values, and two distinct eigen value and 1 repeated eigen value.
Most Upvoted Answer
Consider matrixThe number of distinct real values of k for which the e...
Concept:
We can find the consistency of the given system of equations as follows:
(i) If the rank of matrix A is equal to the rank of an augmented matrix and it is equal to the number of unknowns, then the system is consistent and there is a unique solution.
The rank of A = Rank of augmented matrix = n
(ii) If the rank of matrix A is equal to the rank of an augmented matrix and it is less than the number of unknowns, then the system is consistent and there are an infinite number of solutions.
The rank of A = Rank of augmented matrix < n
Then |A| = 0
(iii) If the rank of matrix A is not equal to the rank of the augmented matrix, then the system is inconsistent, and it has no solution.
The rank of A ≠ Rank of an augmented matrix
Application:
A system to have infinitely many solutions must satisfy:
|A| = 0
K2 (K – 2(K – 1) = 0
K2 (K – 2K + 2) = 0
K2 (-K + 2) = 0
K = 0, 0, 2
Hence, there are 3 eigen values, and two distinct eigen value and 1 repeated eigen value.
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Consider matrixThe number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer?
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Consider matrixThe number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Consider matrixThe number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider matrixThe number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer?.
Consider matrixThe number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Consider matrixThe number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider matrixThe number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________Correct answer is '2'. Can you explain this answer?.
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