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Consider the following two statements with respect to the matrices.
Am×n, Bn×m, Cn×n and Dn×n.
Statement 1 : tr( AB) = tr(BA)
Statement 2 : tr(CD) = tr(DC)
Where tr() represents the trace of a matrix which one of the following holds?
Am×n, Bn×m, Cn×n and Dn×n.
Statement 1 : tr( AB) = tr(BA)
Statement 2 : tr(CD) = tr(DC)
Where tr() represents the trace of a matrix which one of the following holds?
- a)Both statement 1 and 2 are correct.
- b)Statement 1 is true and statement 2 is false
- c)Statement 1 is false and statement 2 is true
- d)Both Statement 1 and 2 are wrong.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Consider the following two statements with respect to the matrices.Am&...
The eigenvalues (counting multiplicity) of AB are the same as those of BA
If A is an m by n matrix and B is an n by m matrix with n ³m then the characteristic polynomial pBA of BA is related to the characteristic polynomial pAB of AB by
Since Eigenvalues are the same thus the sum of Eigen Values (i.e. the Trace) is also the same.
If A is an m by n matrix and B is an n by m matrix with n ³m then the characteristic polynomial pBA of BA is related to the characteristic polynomial pAB of AB by
Since Eigenvalues are the same thus the sum of Eigen Values (i.e. the Trace) is also the same.
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Consider the following two statements with respect to the matrices.Am&...
1. Matrix A is invertible if and only if its determinant is non-zero.
2. If matrix A is invertible, then its row reduced echelon form is the identity matrix.
Statement 1 is true. In linear algebra, a square matrix is invertible if and only if its determinant is non-zero. This means that if the determinant of matrix A is zero, then it is not possible to find an inverse of matrix A.
Statement 2 is not necessarily true. The row reduced echelon form of a matrix is not always the identity matrix, even if the matrix is invertible. However, the row reduced echelon form of an invertible matrix will have a leading 1 in each row and column, with all other entries in the row and column being zero. This is known as the reduced row echelon form (RREF) of the matrix.
2. If matrix A is invertible, then its row reduced echelon form is the identity matrix.
Statement 1 is true. In linear algebra, a square matrix is invertible if and only if its determinant is non-zero. This means that if the determinant of matrix A is zero, then it is not possible to find an inverse of matrix A.
Statement 2 is not necessarily true. The row reduced echelon form of a matrix is not always the identity matrix, even if the matrix is invertible. However, the row reduced echelon form of an invertible matrix will have a leading 1 in each row and column, with all other entries in the row and column being zero. This is known as the reduced row echelon form (RREF) of the matrix.
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Consider the following two statements with respect to the matrices.Am×n, Bn×m, Cn×n and Dn×n.Statement 1 : tr( AB) = tr(BA)Statement 2 : tr(CD) = tr(DC)Where tr() represents the trace of a matrix which one of the following holds?a)Both statement 1 and 2 are correct.b)Statement 1 is true and statement 2 is falsec)Statement 1 is false and statement 2 is trued)Both Statement 1 and 2 are wrong.Correct answer is option 'A'. Can you explain this answer?
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Consider the following two statements with respect to the matrices.Am×n, Bn×m, Cn×n and Dn×n.Statement 1 : tr( AB) = tr(BA)Statement 2 : tr(CD) = tr(DC)Where tr() represents the trace of a matrix which one of the following holds?a)Both statement 1 and 2 are correct.b)Statement 1 is true and statement 2 is falsec)Statement 1 is false and statement 2 is trued)Both Statement 1 and 2 are wrong.Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following two statements with respect to the matrices.Am×n, Bn×m, Cn×n and Dn×n.Statement 1 : tr( AB) = tr(BA)Statement 2 : tr(CD) = tr(DC)Where tr() represents the trace of a matrix which one of the following holds?a)Both statement 1 and 2 are correct.b)Statement 1 is true and statement 2 is falsec)Statement 1 is false and statement 2 is trued)Both Statement 1 and 2 are wrong.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following two statements with respect to the matrices.Am×n, Bn×m, Cn×n and Dn×n.Statement 1 : tr( AB) = tr(BA)Statement 2 : tr(CD) = tr(DC)Where tr() represents the trace of a matrix which one of the following holds?a)Both statement 1 and 2 are correct.b)Statement 1 is true and statement 2 is falsec)Statement 1 is false and statement 2 is trued)Both Statement 1 and 2 are wrong.Correct answer is option 'A'. Can you explain this answer?.
Consider the following two statements with respect to the matrices.Am×n, Bn×m, Cn×n and Dn×n.Statement 1 : tr( AB) = tr(BA)Statement 2 : tr(CD) = tr(DC)Where tr() represents the trace of a matrix which one of the following holds?a)Both statement 1 and 2 are correct.b)Statement 1 is true and statement 2 is falsec)Statement 1 is false and statement 2 is trued)Both Statement 1 and 2 are wrong.Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following two statements with respect to the matrices.Am×n, Bn×m, Cn×n and Dn×n.Statement 1 : tr( AB) = tr(BA)Statement 2 : tr(CD) = tr(DC)Where tr() represents the trace of a matrix which one of the following holds?a)Both statement 1 and 2 are correct.b)Statement 1 is true and statement 2 is falsec)Statement 1 is false and statement 2 is trued)Both Statement 1 and 2 are wrong.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following two statements with respect to the matrices.Am×n, Bn×m, Cn×n and Dn×n.Statement 1 : tr( AB) = tr(BA)Statement 2 : tr(CD) = tr(DC)Where tr() represents the trace of a matrix which one of the following holds?a)Both statement 1 and 2 are correct.b)Statement 1 is true and statement 2 is falsec)Statement 1 is false and statement 2 is trued)Both Statement 1 and 2 are wrong.Correct answer is option 'A'. Can you explain this answer?.
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