1. For the following linear transformation, T, W1 = 3x1 – 6x2 + 2x3 W2 = -2x1 + 4x2 + x3 W3 = X1 - 2x2- x3 W4 = -X1 + 2x2 + 2x3 i) Find the matrix that represents this transformation. ii) Determine the domain of T. aiel Somo TA (vix iii) Determine the codomain of T. iv) Find a basis for ker(T). v) Determine the dimension of the ker(T). vi) Find a basis for range(T). ono-ot-omo T or vii) Determine the dimension of the range(T). Tal Y viii) Is Ta one-to-one mapping? Explain your reasoning. ix) Is T an onto mapping? Explain your reasoning. Determine whether the linear transformation defined by the equations is invertible; if so, find the standard matrix for the inverse transformation, and find T. If it is not invertible, explain why. x)

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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.