Please help understand the problem step by step

Concepts of vector space and change of basis are important to understand this week. They are foundation to understand how to reduce a dimension of a system and the most popular Machine Learning algorithms SVD and PCA so every question is welcome For those who prefer a "question of the week" I wonder do you understand the relationship between a vector and "n-tuple"? I used term "n-tuple" in the lecture to make a distinction between vector spaces: Rnx1 and R1xn They are different in the way we write vectors. There is no distinction between Rnx1 and Rn which allows us to write n-tuples as column vectors x=(x1x2) and row vector is denoted by xT, the transpose of x,xT=(x1x2) Properties of Python's version of a tuple are much like the "n-tuple" representation of a vector space, important property of a tuple is that items are ordered