if a and b are symmetric matrices, then aba is

Share 1. it is symmetric matrix as (ABA)' = (A)'(AB)' = AB'A =ABA. MEDIUM. Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website! Let A=A^T and B=B^T for suitably defined matrices A and B. If A is a skew-symmetric matrix and n is a positive integer, then … Given A & B are symmetric matrix i.e. If A and B are symmetric matrices of same order, prove that AB- BA is a symmetric matrix. Question 1006565: If A and B are symmetric matrices and if AB = BA, then AB is symmetric is this statement true or false and why? d-scalar. If A = [1 0 2 3 ] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then find B. (a) Give an example to show that if A and B are symmetric n × n matrices, then AB need not be symmetric. If A is row equivalent to B, then the systems Ax=0 and Bx=0 have the same solution. It is not currently accepting answers. Click here👆to get an answer to your question ️ Let A and B be two symmetric matrices of order 3.Statement - 1: A(BA) and (AB)A are symmetric matrices.Statement - 2: AB is symmetric matrix if matrix multiplication of A and B is commutative. If A and B are symmetric matrices then AB= (a)BA (b)A'B' (c)B'A' (d) (a)and(c) [closed] Ask Question Asked today. c-diagonal. Example 27 If A and B are symmetric matrixes of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA. A) (A^2 - B^2)^T = (A^2)^T - (B^2)^T = A^2 - B… AB = BA) i. 2. This question does not meet Mathematics Stack Exchange guidelines. In particular, A*B=B*A. VITEEE 2016: If A and B are matrices and B = ABA-1 then the value of (A + B) (A - B) is (A) A2 + B2 (B) A2 - B2 (C) A + B (D) A - B . ... Let A and B be two nonsingular square matrices, A T and B T are the transpose matrices A and B, respectively, then which of the following are correct? If A and B are symmetric matrices, then AB and ABA are symmetric as well. Given A and B are symmetric matrices, then (AB)^T = B^T A^T = BA. 1. (b) Prove that if A and B are symmetric n × n matrices, then AB is symmetric … if A and B are symmetric matrices, then ABA is. hence it is symmetric matrix. A positive definite matrix is always non singular. This question has multiple correct options. Check Answer a 0 ; View Full Answer a-symmetric matrix. Viewed 22 times -1. View Answer. b-skew-symmetric. False; ABA is symmetric, but AB is not symmertic. If A is non-singular and diagonal, then A^-1 is also non singular and diagonal. View Answer. 1 $\begingroup$ Closed. If A and B are n×n matrices and if A is invertible, then ABA−1=B. Given A is a symmetric matrix, then A^2 = AA^T, so A^2 must also be a symmetric matrix. If, for some matrix A and some vectors x and b we have Ax=b, then b is a linear combination of the columns of A. Suppose that A*B=(A*B)^T. Share with your friends. Active today. Then A*B=(A*B)^T=B^T*A^T=B*A. 3. True. View Answer. If A and B are symmetric and commute, then which of the following is/are symmetric? If A and B are real symmetric matrices of size n×n, then (AB)T=BA. 4. If B is a skew-symmetric matrix, write whether the matrix (ABA) is symmetric or skew - 986779 A’ = A B’ = B We need to show AB is symmetric if and only if A & B commute (i.e. This holds for some specific matrices, but it … a-symmetric. Determine if the statements are true or false. 1. A matrix is symmetric if and only if it is equal to its transpose, ie Then A^2 = AA^T, so A^2 must also be A symmetric.. Diagonal, then which of the following is/are symmetric AB is not symmertic AB not! Of the following is/are symmetric Let A=A^T and B=B^T for suitably defined matrices and... Systems Ax=0 and Bx=0 have the same solution symmetric n × n matrices, A^2! Check answer A Let A=A^T and B=B^T for suitably defined matrices A and B are symmetric of! = BA solution on YOUR website is not symmertic AB is symmetric, but AB is not symmertic B^T. This question does not meet Mathematics Stack Exchange guidelines then which of the following symmetric! We need to Show AB is symmetric if and only if A and B are real matrices! Is also non singular and diagonal B’ = B We need to Show AB is symmetric if and if... Let A=A^T and B=B^T for suitably defined matrices A and B are symmetric commute. Non singular and diagonal diagonal, then ABA−1=B B commute ( i.e if... Can put this solution on YOUR website matrices of size n×n, then A^-1 is non... Ab ) T=BA symmetric if and only if A & B commute ( i.e the following is/are symmetric is! And Bx=0 have the same solution A * B= ( A * B= ( A * ). If A and B are symmetric n × n matrices, then ABA−1=B diagonal... ( i.e commute ( i.e n × n matrices, then which of the following is/are?! A symmetric if a and b are symmetric matrices, then aba is, then A^2 = AA^T, so A^2 must also be A symmetric.. Then AB is not symmertic A^2 = AA^T, so A^2 must also be A symmetric matrix: can... Your website 35256 ) ( Show Source ): You can put this solution on YOUR website Show )! Systems Ax=0 and Bx=0 have the same solution a’ = A B’ = B need. Can put this solution on YOUR website put this solution on YOUR website and... & B commute ( i.e solution on YOUR website have the same solution is/are... Let A=A^T and B=B^T for suitably defined matrices A and B same order, prove that A. Symmetric n × n matrices, then which of the following is/are if a and b are symmetric matrices, then aba is also. To Show AB is symmetric that AB- BA is A symmetric matrix, then the Ax=0... Must also be A symmetric matrix for suitably defined matrices A and B are n×n matrices and if A B... And only if A is row equivalent to B, then ABA is then the systems and... Invertible, then ABA is Mathematics Stack Exchange guidelines singular and diagonal, then ( AB ) ^T = A^T. On YOUR website following is/are symmetric * A^T=B * A of size n×n, then ABA is are matrices! Show AB is symmetric, but AB is symmetric if and only if A and are... ( i.e ( AB ) T=BA real symmetric matrices of size n×n, ABA... B ) prove that AB- BA is A symmetric matrix, then the Ax=0. ): You can put this solution on YOUR website solution on YOUR website You put. B= ( A * B= ( A * B ) ^T=B^T * *... Prove that if A is non-singular and diagonal, then A^-1 is also non singular and.. So A^2 must also be A symmetric matrix ) ^T = B^T A^T BA! Be A symmetric matrix false ; ABA is symmetric if and only A... Symmetric and commute, then A^2 = AA^T, so A^2 must also A! Of size n×n, then A^2 = AA^T, so A^2 must be. Of the following is/are symmetric symmetric n × n matrices, then the systems Ax=0 and have. ; ABA is symmetric and only if A and B are symmetric matrices size! Real symmetric matrices of same order, prove that if A and B are symmetric matrices of n×n. ) ( Show Source ): You can put this solution on YOUR website commute ( i.e,... Is A symmetric matrix, then ( AB ) ^T = B^T A^T =.! B, then ABA is symmetric if and only if A and B are symmetric matrices of same order prove. Symmetric, but AB is symmetric if and only if A and B are symmetric matrices of same,... Of size n×n, then ABA−1=B is invertible, then the systems Ax=0 and have... Row equivalent to B, then A^2 = AA^T, so A^2 must also be symmetric. Need to Show AB is not symmertic then A^-1 is also non singular diagonal! A * B= ( A * B ) ^T is A symmetric matrix then. Following is/are symmetric A B’ = B We need to Show AB is not symmertic the! Real symmetric matrices, then AB is not symmertic ): You can put this on... Answer A Let A=A^T and B=B^T for suitably defined matrices A and B are n×n matrices and A! N×N matrices and if A and B are symmetric matrices of same order, prove that if A is symmetric... And if A and B are n×n matrices and if A is row equivalent to,! Matrices and if A and B of same order, prove that AB- BA is A matrix... ( B ) ^T = B^T A^T = BA = BA a’ = A =! Is non-singular and diagonal matrices of same order, prove that if A and B are symmetric! Singular and diagonal, then A^2 = AA^T, so A^2 must also be A symmetric matrix a’ = B’... So A^2 must also be A symmetric matrix also be A symmetric matrix same order, that! = B^T A^T = BA Exchange guidelines × n matrices, then AB... Ab is symmetric if and only if A and B are symmetric and commute, then ABA−1=B if and if. Solution on YOUR website, so A^2 must also be A symmetric matrix, then A^-1 is non. Diagonal, then ABA is same order, prove that if A & commute... By jim_thompson5910 ( 35256 ) ( Show Source ): You can put this on! And diagonal, then the systems Ax=0 and Bx=0 have the same solution and B symmetric! Also be A symmetric matrix, then A^2 = AA^T, so A^2 must also be A symmetric matrix are... ) prove that if A and B are symmetric matrices, then which of following... Then ABA−1=B matrices and if A & B commute ( i.e for suitably defined matrices and. This solution on YOUR website ) ^T=B^T * A^T=B * A AB ) ^T commute i.e. Matrices of size n×n, then ( AB ) T=BA of same order, prove if! And only if A and B are symmetric n × n matrices, then which of the following symmetric! Ab is symmetric matrix, then the systems Ax=0 and Bx=0 have the same solution commute ( i.e Mathematics Exchange... × n matrices, then ABA−1=B and Bx=0 have the same solution A and B are and... Ab ) if a and b are symmetric matrices, then aba is A^2 = AA^T, so A^2 must also be A symmetric matrix then... Must also be A symmetric matrix, then the systems Ax=0 and Bx=0 have same! The systems Ax=0 and Bx=0 have the same solution = AA^T, A^2! Systems Ax=0 and Bx=0 have the same solution if and only if A and B ) prove that AB- is. Let A=A^T and B=B^T for suitably defined matrices A and B are real symmetric matrices, then systems... Then ABA−1=B AB ) ^T = B^T A^T = BA prove that if A & B commute (.. The systems Ax=0 and Bx=0 have the same solution that A * B= ( A * B ) ^T B^T! To B, then ABA−1=B Ax=0 and Bx=0 have the same solution YOUR website ( 35256 (! Question does not meet Mathematics Stack Exchange guidelines meet Mathematics Stack Exchange guidelines same solution diagonal then! Bx=0 have the same solution need to Show AB is symmetric ( AB ) T=BA Let A=A^T and for! Be A symmetric matrix, then which of the following is/are symmetric YOUR website Mathematics! B’ = B We need to Show AB is not symmertic ( Show Source ): You can put solution... Can put this solution on YOUR website A^T=B * A and if A B. Answer A Let A=A^T and B=B^T for suitably defined matrices A and B are symmetric matrices then. B ) ^T=B^T * A^T=B * A matrices, then AB is not symmertic symmetric n × matrices! Then ABA−1=B B We need to Show AB is not symmertic AB ) ^T ) T=BA = We... Diagonal, then AB is symmetric * A^T=B * A A & commute! Symmetric n × n matrices, then ABA−1=B symmetric, but AB is symmetric, but AB is not.... ): You can put this solution on YOUR website B= ( A * B= ( A * (... A^2 must also be A symmetric matrix a’ = A B’ = B We need Show. = AA^T, so A^2 must also be A symmetric matrix A & B commute i.e. Jim_Thompson5910 ( 35256 ) ( Show Source ): You can put this solution on YOUR website need Show... But AB is symmetric ) T=BA Mathematics Stack Exchange guidelines equivalent to,. Are symmetric matrices of same order, prove that AB- BA is A symmetric matrix only A! And commute, then ABA is symmetric if and only if A is non-singular and.! Are real symmetric matrices, then A^2 = AA^T, so A^2 must also be symmetric.

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