An idempotent matrix M is a matrix such that M^2=M. Add your answer and earn points. The volume of a sphere with radius r cm decreases at a rate of 22 cm /s  . Exercise problem/solution in Linear Algebra. 1 answer. There is such a thing as a complex-symmetric matrix ( aij = aji) - a complex symmetric matrix need not have real diagonal entries. If A And B Are Symmetric Matrices of the Same Order, Write Whether Ab − Ba Is Symmetric Or Skew-symmetric Or Neither of the Two. If A is a symmetrix matrix then A-1 is also symmetric. In a game, where 5 dice are tossed simultaneously, find the probability of getting 4 of a kind. This problem has been solved! Hence, the correct option is (a). If A and B are symmetric matrices, then find BA − 2AB . In this video, we define a symmetric matrix and prove that for symmetric matrices A and B, AB is symmetric if and only if AB=BA.. …, hey friends. Question Papers 1786. ∴ Correct answer is A. CBSE CBSE (Commerce) Class 12. 1 answer. WHO has guidelines. If A and B are two symmetric matrices and they follow the commutative property, i.e. See the answer. Show that if A and B are square matrices such that AB = BA, then (A+B)2 = A2 + 2AB + B2 . Ex 3.3, 11 If A, B are symmetric matrices of same order, then AB − BA is a A. A matrix is symmetric if and only if it is equal to its transpose, ie X = X^T Given: A = A^T (since matrix A is symmetric) B = B^T (matrix B is symmetric) AB = BA We want to prove: AB is symmetric ie, AB = (AB)^T AB = BA AB = B^T*A^T ... use the given info above AB = (AB)^T ... use property 3 So the claim has been proven true. Show detailed proofs on the following: 1. If A and B are symmetric matrices then AB+BA is a symmetric matrix (thus symmetric matrices form a so-called Jordan algebra). Show that AB is symmetric. Suppose that A*B=(A*B)^T. Prove that AB = BA if and only if AB is also symmetric. Given, A ,B is symmetric so, A=A', B=B' now, ( AB+BA)`=(AB) `+(BA) `=B'A'+A'B'=(BA+AB)=(AB+BA) so, (AB+BA)`=AB+BA it's symmetric, hence proved. Let A=A^T and B=B^T for suitably defined matrices A and B. 1. {3 marks} Let A, B be n × n matrices. The graphs of Sine and Cosine are positive in the first quadrant, but negative in the second, third, and fourth quadrants.? A square matrix A=[aij] is said to be symmetric if A'=A that is [aij]=[aji] for all possible value of i and j. The sum and difference of two symmetric matrices is again symmetric This is not always true for the product: given symmetric matrices A{\displaystyle A}and B{\displaystyle B}, then AB{\displaystyle AB}is symmetric if and only if A{\displaystyle A}and B{\displaystyle B}commute, i.e., if … Does anyone know what the solution would be to geometry question: AB = 10 and CD = 18. 2. Transcript. The simplified value of log, 4√72 A square matrix A=[aij] is said to be skew symmetric if A'=-A that is [aij]=−[aji] for all possible value of i and j. Important Solutions 3417. If we multiply a symmetric matrix by a scalar, the result will be a symmetric matrix. On the other hand, if AB = BA, then we have AB = BA = BTAT = (AB)T. Thus, we have AB = (AB)T, hence AB is symmetric. Then A*B=(A*B)^T=B^T*A^T=B*A. Addition and difference of two symmetric matrices results in symmetric matrix. Thus, if A and B are both n x n symmetric matrices then AB is symmetric ↔ AB = BA. The sum of two symmetric matrices is a symmetric matrix. Give an example of a symmetric matrix order 3×3. How much exercise do you need? = AB-1 [as A = A′ (symmetric) and (B-1)′ = (B′)-1 = B-1] Hence, AB-1 is symmetric. Skew symmetric matrix B. Symmetric matrix C. Zero matrix D. Identity matrix A and B are symmetric matrices, ∴ A’ = A and B’ = B Consider (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ = BA − AB = − (AB – BA) ∴ (AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. Nashville ICU nurse shot dead in car while driving to work, NBA star chases off intruder in scary encounter, White House signals no rush on coronavirus stimulus, Cyrus says marriage was 'last attempt to save' herself, Children's museum sparks backlash for new PB&J cafe, Pence tells Georgia voters election still undecided, Report: Ex-NBA star sued by weed consultant, Capitalism 'will collapse on itself' without empathy and love, David Lander, Squiggy on 'Laverne & Shirley,' dies at 73. Disclaimer: There is a misprint in the question.It should be BA T instead of B T A. Suppose that A,B are non null matrices and AB = BA and A is symmetric but B is not. Recall that a matrix C is symmetric if C = C^t where C^t denotes the transpose of C. = B^tA^t; by how the transpose "distributes". A and B are symmetric matrices → A=A' →B=B' BA-2AB is a neither symmetric nor skew symmetric matrix. = AB; by assumption. Suppose that AB=BA where A, B are symmetric. See Answer. Since AB is symmetric, we have AB = (AB) T But (AB) T = B T A T Hence AB = B T A T …(1) It is also given that A and B are symmetric A T = A and B T = B Hence (1) becomes, AB = BA Thus AB is symmetric if and only if AB = BA.