3. -4 points 3.2.036. 0/3 Submlssions Used an example to show that if A and 8...
QUESTION 6 a) Prove the product of 2 2 x 2 symmetric matrices A and B is a symmetric matrix if and only if AB=BA. b) Prove the product of 2 nx n symmetric matrices A and B is a symmetric matrix if and only if AB=BA.
[1 2 37 1. Is the matrix 1 0 1 invertible? If yes, what is its inverse? [O 2 -1 2. A matrix is called symmetric if At = A. What can you say about the shape of a symmetric matrix? Give an example of a symmetric matrix that is not a zero matrix. 3. A matrix is called anti-symmetric if A= -A. What can you say about the shape of an anti- symmetric matrix? Give an example of an...
13 please
8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3 0-2 0 3 0 0 -2 0 3 0 4 o0-1 6 0 0 1 o 2 6 0 0 -1 6 10. For any positive integer k, prove that det(4t) - de(A)*. 11. Prove that if A is invertible, then den(A-1)- I/der(A) - det(4)- 12. We know in general that A-B丰B-A for two n x n matrices. However, prove that: det(A . B)-det(B...
Q3 (3 points) Show that if both AB and B A are defined then AB and BA are square matrices. + Drag and drop your images or click to browse... Q4 (3 points) Let A = (a) be a 2 x 2 matrix. The trace of A. which we denote by tr(A) is a number defined as tr(A) = 0 + 0x2. Prove the following properties of this number for 2 x 2 matrices A and B and a real...
In Exercises 3-4, use the Subspace Test to determine which of the sets are subspaces of Mnn. 3. a. The set of all diagonal n x n matrices. b. The set of all n × n matrices A such that det(A) = 0. c. The set of all n × n matrices A such that tr(A) = 0. d. The set of all symmetric n × n matrices.4. a. The set of all n × n matrices A such that AT = -A. b. The set...
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-A-t +1 where t = Tr(A).
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove...
Consider the following matrices: 1 2 A= 3-4 2 3 B= 3 2 1 1 0 2 C= 2 1 3 -1 1 1 1 4 5 -4 2 5 1 3 4 1 0 1 1 - 2 D= E= F 4 1 31 7 3 2 Find each of the following, if possible. If it is not possible, explain your reasoning. 1 (a) AB (9) BAT (b) BA (h) (A + B) E (C) CD + E ()...
3.23 True or false. justify your answer
190 LINEAR TRANSFORMATIONS 3.22 Let A be a 4 x 3 matrix and B a 3 x 4 matrix. Then AB cannot be in 3.23 Suppose that A is an invertible matrix and B is any matrix for which BA i 3.24 Suppose that A is an invertible matrix and B is any matrix for which AB is 3.25 Suppose that A and B are nxn matrices such that AB is invertible. Then...
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
Give an example that C is false. This will count for the 4
points in this problem
I. (a) (1 point(Truen False: Let A be a square matrix. If det(A) =-1 then A is invertible False ret A be the rotation matrix of a vector by the angle ф (b) (1 point) True and B the rotation matrix of a vector by the angle 0 Then: AB represents the rotation by the angle ф* (e) (1 point) True or False:...