Problem 1: Let 1 -1 1 1/4 -1/2 1 A = 1 1/4 -1/2 1 1 1 1 Part I: Find a basis of orthonormal vectors for Range(A) using the Gram-Schmidt orthogonalization process. Part II: From your calculations of Part I, find a QR factorization of A where the columns of Q are orthonormal vectors and R is an upper triangular matrix. Part III: Solve the least square problem Ar = b where b = [1 1/2 1 1/2 1]". The QR factorization of Part II can be used for this. Is the solution that you determined in Part III, unique, or are there other possible solutions of the least square problem? Give a brief explanation for your answer.

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A: Hello! Thank you for the question. We'll able to solve only one question as per our honor code.

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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.