Let As(4-1) md-G) (a) Compute A + B, if definded. If not defined, say so and...
Need help!! 1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of...
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...
We say that A and B are similar matrices if A = SBS-1 for some invertible matrix S. Are the following true or false. Given a mathematical reason (proof). (a) If A and B are similar, then A and B have the same eigenvalues. Answer: (b) If A and B are similar, then A and B have the same eigenvectors. Answer: c) If A and B are similar, then A - 51 and B – 51 are similar. Answer: (d)...
Problem 4 a) Let A and B be nxn matrices with an eigenvalue for A and i an eigenvalue for B. Is + i necessarily an eigenvalue for A +B? Is di necessarily an eigenvalue for AB? If so, explain why. If not, come up with a counterex- ample. What if and i have the same eigenvector x? b) If A and B are row equivalent matrices, do they have the same eigenvalues? If so, explain why. If not, give...
Both problems (1 point) Solve for X. ]+sx= [=] X = (1 point) Let A be a 5 by 6, B be a 6 by 7 and C be a 7 by 5 matrix. Determine the size of the following matrices (if they do not exist, type N in both answer boxes): AB: BA: A+B: BC: ABC: CA: B? A: BCT:
I will rate if correct 4. (10 pts) Let A,B be square matrices with the same size n × n, and let c be a constant. True or False: (a) (AB)-1- B-1A-1 (b) ABメBA in general. (c) det(AB) = det(B) * det(A) (d) (CAB)1A (e) rank(A+ B) S rank(A) + rank(B)
Let D4 be dihedral group order 8. So D4={e, a, a^2, a^3, b, ab, a^2b, a^3b}, a^4 = e, b^2= e, ab=ba^3; A. FIND ALL THE COSETS OF THE SUBGROUP H= , list their elements. B. What is the index [D4 : H] C. DETERMINE IF H IS NORMAL
Let A and E be matrices with the following sizes.A: 3 × 4 E: 4 × 3 If defined, determine the size of the matrix E − 2A. (If an answer is undefined, enter UNDEFINED.) × If not defined, explain why. E − 2A is defined. E − 2A is not defined because E and 2A have different sizes. E − 2A is not defined because E and 2A have the same size. E − 2A is not defined because the...
[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...
1. (a) Let T:R' R'be defined by T(x) = 5 -2. Is T a linear transformation? If so, prove that it is. If not, explain why not. (b) More generally than part (a), suppose that T:R → R is defined by T(x) = ax +b, where a and b are constants. What must be true about a and b in order for T to be a linear transformation? Explain your answer.