#5 Proof Please 5. Perfect Proof. If A is an invertible operator on a finite dimensional vector space V then there is a polynomial p so that p(A) = A-!. HINT: Find a non-zero polynomial q of least degree so that q(A) - 0. (What is dimension of C(VV)?) Show that the constant term of q is not zero.
Complete the proof. [}proof{]; 1. AvB, premise; 2.A>(C&D), premise; 3.B>(~C&D),premisel:D>C Answer: efs in Three Jump to... ns Complete the proof. [}proof{l; 1. (A&B)>C, premise; 2.B,premisel:~AVC Answer: Complete the proof. [}proof{]; 1.A,premise; 2.Bvc, premise| : ~(A&B)>(A&C) Answer:
Consider the following algebraic proof to show the identity: -(s v w) (-SA w)= ~S. Proof. Let s and w be any two statement forms, -(s v w) (-SA W)=(-SA-w)v(~SAW) =-SA(-wvw) =-SA (wv -W) -Sat ES Select the law that justifies the step: (SAW) v(~SAW) = -SA(-wvw) Distributive Law De Morgan's Law Identity Law Negation Law
Problem 3 (3 points) Use proof by induction to prove the Bonferroni's inequality (for any positive integer n): Si<jSni.jez
(Mathematical analysis w/ proof) please explain and don't skip any steps Prove that f(x) = x + lis uniformly continuous on (0, 2 - 1
1. Prove the following statements (a) (1 point) If A is invertible, prove that Ak is invertible for any k > 1. (b) (1 point) Assuming A is invertible, prove that det((A*)-1) = (det(A))** (e) (1 point) Prove that det(QA) = a det(A), A € Mmxm(R), a € R, using the definition of the determinant (Hint: you may have seen this problem already in this course). (a) (1 point) Prove that if J is the Jordan normal form of A,...
Q3 Let A = {a,b,c} and Aº = {abcw1W2 ---W | W; E A for all i > 1} denote the set of all infinite length strings over A that start with the “abc" substring. That is, each string A™ is an infinite sequence of characters "abcw1W2 ... Wo" where each wie A. Prove that Aº is not countable using a proof by contradiction that includes a diagonalization argument.
Which of the following reactions is a nonredox reaction? | a) CaCO3 --> CaO + CO2 b) 2 KCIO3 ----> 2 KCI + 3 02 c) CaS + H2O --> CaO + 2 H2S d) Zn + CuCl2 ---> ZnCl2 + Cu e) HNO3 + KOH ----> KNO3 + H20 ) ) a) and b) g) b) and c) h) a) and d) i) d) and e) 0 ) a) and c) and e) 4 k) no correct response (i.e....
w or why not Exercise 2.1.33 Suppose AB - AC and A is a non invertible nxn matrix. Does it follow that B Explain why or why not C ? Exercise 214 Ci c le 42
e. -1135 Given the following reactions: CaCO3 (s)-> Cao (s) + CO2 (g) C (s, graphite) + O2 (g)-> Co2 (g) AH-393.5 kJ the enthalpy of the reaction CaCO3 (s) -> CaO (s) + C (s, graphite) + O2 (g) ΔH = 178.1 kJ is kJ Select one: 4 a. 7.01 x 10 b. 571.6 ) c. 215.4 d. -215.4 ie. -571.6 Check Given the data in the table below, AH for the reaction