Let M2(R) be the set of 2 x 2 matrices with real entries. That is: {[: a b M2(R) = Let S2(R) be the set of 2 x 2 symmetric matrices with real entries. That is: S;(R) = {| T, y, z, w & y = Let D2(R) be the set of 2 x 2 diagonal matrices with real entries. That is: DAR) = {[; : mreR}. u 0 1. Prove that D2(R) C S2(R).

Q: Question Show. is Banach space

A:

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (AU B) exists if sup(B)…

A: If s is an upper bound for A∪B iff it is an upper bound for A and for B, so s≥supA and s≥supB   The…

Q: Find isomorphic spaces O R and R² O P3 and M2x1 O P3 and M2×3 O P3 and R2 O R' and M2×2

A: We have to choose whether the given spaces are isomorphic or not.

Q: If geRfabland if hex)=gox) except fos of finive number of number Point in fab?, then prove…

A: The given partition should be first divided into finite partitions.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.