Problem #1 [10 Points] Let A E Rnxn, B E Rnxm and show that if a vector r1 E R" satisfies zi Range B, AB,.... A-iB 岔1 then Azi E Range [B, AB,...,A-B
2. Let A e cnxn and A BiC, where B,C E Rnxn and i -I. Denote B -C (a) Show that A is unitary if and only if M is orthogonal. (b) Show that A is Hermitian positive definite if and only if M is symmetric positive definite. (c) Suppose A is Hermitian positive definite. Design an algorithm for solving Ar-busing real arithmetic only 2. Let A e cnxn and A BiC, where B,C E Rnxn and i -I. Denote...
4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B 1-A and A2 = A. Show that AB-BA-0 4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B...
Let traingle ABC have midpoint B' on AC, C' midpoint of AB and G be centroid. If AC=5, AB=5, and CC'=6 find BC.
5. Prove or disprove the following statements (a) Let A B and C be 2 x 2 matrices. If AB = AC, then B = C (b) If Bvi,.., Bvh} is a then vi, . ., vk} is a linearly independent set in R". linearly independent set in R* where B is a kx n matrix, 5. Prove or disprove the following statements (a) Let A B and C be 2 x 2 matrices. If AB = AC, then B...
please answer 17c and 17d. 17. Show that the following Post correspondence systems have no solutions. a) [b, ba], [aa, b], [bab, aa], [ab, ba] b) [ab, a]. [ba, bab], [b, aa], [ba, ab] c)lab, aba] lbaa, aa]. [aba. baal (dy [ab, bb], [aa, ba]. [ab, abb]. [bb, bab] e) [abb, ab], [aba, ba], [aab, abab] 17. Show that the following Post correspondence systems have no solutions. a) [b, ba], [aa, b], [bab, aa], [ab, ba] b) [ab, a]. [ba,...
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X,...
Consider the rules AB -> C, AC -> B, BC -> A, where A,B,C are three items. The support for all the 3 rules is the same. a) TRUE b) FALSE
Simplify Y = AB’ + (A’ + B)C. a) AB’ + C b) AB + AC c) A’B + AC’ d) AB + A