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Is thi set of vectors, $\ { (2, 1), (3, 2), (1, 2)\}$, is linearly . . . When you have vectors like $\displaystyle\left [\begin {array} {c}1\\2\end {array}\right]=1\mathbf {i}+2\mathbf {j}$, they live on the plane where there are essentially two different directions: left right ($\mathbf {i}$) and up down ($\mathbf {j}$) Every other direction can be made out of combinations of left right and up down; e g $1\mathbf {i}+2\mathbf {j}$ Now for a set to be linearly
How do the definitions of irreducible and prime elements differ? You are correct in observing that your lecture notes are not quite right here It is indeed the definition of an irreducible element What you read elsewhere is indeed the definition of prime element
Given a 95% confidence interval why are we using 1. 96 and not 1. 64? The Z-score for 90% is -1 6444 and 1 6444 , 1 sigma The z-score for 95% is -1 96 and 1 96 , 2 sigma The z-score for 99% is -2 5758 and 2 5758 , 3 sigma in your Estimation of Population Mean meaning, that mean plus or minus 1 96 times its standard deviation gives 95% C I Errors distr estimation is considered to use t-distr with fatter tails than Normal distr , but with increasing size of
What does versus mean in the context of a graph? The answer (as is often the case) come from Latin "versus" simply means against and is used in the sporting context as well We say that in some contest "Team A versus team B", meaning team A is against team B The graph is the same - one variable is plotted against (or versus) another From the same cognate root we also get the English "adversary"