Let X1, X2, and x3 be vectors in R3. If x1 is perpendicular to X2 and X2 is perpendicular to x3, is it necessarily true that x1 is perpendicular to x3? Prove your
answer.

Which themes are portrayed in this excerpt from leo tolstoy’s the death of ivan ilyich? praskovya fedorovna came of a good family, was not bad looking, and had some little property. ivan ilyich might have aspired to a more brilliant match, but even this was good. he had his salary, and she, he hoped, would have an equal income. she was well connected, and was a sweet, pretty, and thoroughly correct young woman. to say that ivan ilyich married because he fell in love with praskovya fedorovna and found that she sympathized with his views of life would be as incorrect as to say that he married because his social circle approved of the match. he was swayed by both these considerations: the marriage gave him personal satisfaction, and at the same time it was considered the right thing by the most highly placed of his associates. so ivan ilyich got married. conforming to social conventions criticism of a middle class lifestyle the destructive impact of loneliness struggling to face reality the necessity of companionship

Whats are the trickiest steps to do when adding or subtracting rational expressions? how does knowledge of rational numbers u in adding and subtracting rational expressions?

Prove that 16^4-2^13-4^5 is divisible by 11.