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Let A be an n-by-n matrix with coefficients in F, having rows{a1, ..., an). Then which one of the statement is true for the matrix A?
  • a)
     A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then D(A’) = –D(A)
  • b)
     A’ be a matrix obtained from A by an elementary row operation (replacing the row ai by ai + λaj , with λ ∈ F, i ≠ j).  Then D(A’) = D(A)
  • c)
     A’ be a matrix obtained from A by an elementary row operation (replacing ai by µaj , for µ ≠ 0 in F).  Then D(A’) = µD(A). 
  • d)
     All the three options are correct.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let A be an n-by-n matrix with coefficients in F, having rows{a1, ...,...
By a well known result we know that if A be an n × n matrix with coefficients in F, having rows {a1, a2, ....., an }, then the following statements are true. 
 (a) if A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then 
 D(A’) = – D(A) 
 (b) if A’ be a matrix obtained from a by an elementary row operation (replacing the row ai by λaj , with λ ∈ F, i ≠ j). Then 
D(A’) = D(A) 
(c) if A’ be a matrix obtained from A by an elementary row operation (replacing ai by µai , for µ ≠ 0 in F). Then 
 D(A’) = µD(A)
i.e. all the three options are correct. 
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Let A be an n-by-n matrix with coefficients in F, having rows{a1, ..., an). Then which one of the statement is true for the matrix A?a)A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then D(A’) = –D(A)b)A’ be a matrix obtained from A by an elementary row operation (replacing the row ai by ai + λaj , with λ ∈ F, i ≠ j). Then D(A’) = D(A)c)A’ be a matrix obtained from A by an elementary row operation (replacing ai by µaj , for µ ≠ 0 in F). Then D(A’) = µD(A).d)All the three options are correct.Correct answer is option 'D'. Can you explain this answer?
Question Description
Let A be an n-by-n matrix with coefficients in F, having rows{a1, ..., an). Then which one of the statement is true for the matrix A?a)A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then D(A’) = –D(A)b)A’ be a matrix obtained from A by an elementary row operation (replacing the row ai by ai + λaj , with λ ∈ F, i ≠ j). Then D(A’) = D(A)c)A’ be a matrix obtained from A by an elementary row operation (replacing ai by µaj , for µ ≠ 0 in F). Then D(A’) = µD(A).d)All the three options are correct.Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let A be an n-by-n matrix with coefficients in F, having rows{a1, ..., an). Then which one of the statement is true for the matrix A?a)A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then D(A’) = –D(A)b)A’ be a matrix obtained from A by an elementary row operation (replacing the row ai by ai + λaj , with λ ∈ F, i ≠ j). Then D(A’) = D(A)c)A’ be a matrix obtained from A by an elementary row operation (replacing ai by µaj , for µ ≠ 0 in F). Then D(A’) = µD(A).d)All the three options are correct.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A be an n-by-n matrix with coefficients in F, having rows{a1, ..., an). Then which one of the statement is true for the matrix A?a)A’ be a matrix obtained from A by an elementary row operation (interchanging two rows). Then D(A’) = –D(A)b)A’ be a matrix obtained from A by an elementary row operation (replacing the row ai by ai + λaj , with λ ∈ F, i ≠ j). Then D(A’) = D(A)c)A’ be a matrix obtained from A by an elementary row operation (replacing ai by µaj , for µ ≠ 0 in F). Then D(A’) = µD(A).d)All the three options are correct.Correct answer is option 'D'. Can you explain this answer?.
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