Determine which of the formulas hold for all invertible n X n matrices A and B B. (A B2- A2 + B2 +2AB D.A +B is invertible E.ABA-1B F9A is invertible Determine which of the formulas hold for all invertible n X n matrices A and B B. (A B2- A2 + B2 +2AB D.A +B is invertible E.ABA-1B F9A is invertible
Does the identity (a+b)(a-b)=a2-b2 hold in the ring M2(R) of 2x2-matrices with real coefficients?
(a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that P(A1|B1).P(A2|B2)=P(A1|B2).P(A2|B1). (b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1∪B2 are independent if and only if A and B1∩B2 are independent. (c) Given P(A) = 0.42,P(B) = 0.25, and P(A∩B) = 0.17, find (i)P(A∪B) ; (ii)P(A∩Bc) ; (iii)P(Ac∩Bc) ; (iv)P(Ac|Bc).
Substances A2, B2, and C2 can all act as oxidizing agents. In solution, A2 is green, B2 is yellow, and C2 is red. In the reactions in which they participate, they are reduced to A-, B-, and C ions, all of which are colorless. When a solution of B2 is mixed with one containing C ions, the color changes from yellow to red. a. Which species is oxidized? b. Which is reduced? When a solution of B2 is mixed with...
2. (a) Let P(Bin B2) > 0, and AUA, CBin B2. Then show that P(A/B).P (A2|B2) = P(A|B2).P (A2|Bi). (b) Let A and Bbe independent; similarly, let A and B, be independent. Show that in this case, A and B U B2 are independent if and only if A and Bin B2 are independent (c) Given P(A) = 0.42, P(B) = 0.25, and P(An B) = 0.17, find (i) P (AUB); (ii) P(An B°); (iii) P(A n B); (iv) P(...
Prove that ab ≤ 1/2(a2 + b2) for any real numbers a and b.
cos2θ = (2ab)/(a2 + b2). Find the values of a and b.
For the reaction A2(g) + B2(g) <=> 2AB(g), calculate the value for Kc at 25oC if [A] = 1.073M, [B] = 1.112M, and [AB] = 24.1M. (assume a minimum of 3 significant figures for each molarity).
2. Consider the reaction A2 + B2 ⇌ 2AB. If the initial concentration of both A2 and B2 is 4.0 M, and after 10 minutes the reaction appears to stop. The concentration of [A2] is now 2.0M. a. Draw a graph of [A2] vs. time, over the span of 20 minutes. b. On the same axes draw a graph of [B2] v time, over a span of 20 minutes. c. On the same axes draw a graph of [AB] v...
2. Consider the reaction A2+ B2 = 2AB. If the initial concentration of both A2 and B2 is 4.0 M. and after 10 minutes the reaction appears to stop. The concentration of [A2) is now 2.0M. a. Draw a graph of [A2) vs. time, over the span of 20 minutes. 09. (M concertuohon 5 15 20 time (min) b. On the same axes draw a graph of [B2] v time, over a span of 20 minutes. c. On the same...