(a) Consider the system Mx = v, where 2 6 1 4 4 1 3 M = 4 8-4 4 2 0 2 and v = (0,-2, 8, 3)". The augmented matrix is given in reduce row echelon form by /1 0 0 1 0 10 - 0 0 1 - 3 rref([M|v]) = 0 0 0 0 (i) Find a basis for Col M. (ii) Determine if the system Mx = v is consistent or inconsis tent. Explain your answer, and give clear references to any theorems you use. (b) Show, by finding a suitable example, that for two matrices A anc B, rank(A) = rank(B) does not imply rank(A2) = rank(B2). %3D %3D 1/2 MI2

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A: Sample size (n) = 10 Probability(p) = 0.69

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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.